Newsgroups: rec.puzzles Followup-To: sci.arithmetic From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 2 Jan 92 20:10:09 GMT Subject: Re: Convergent/Divergent series yo...@cbnews.cb.att.com (yossi.a.nygate) writes: >1) If the harmonic series diverges, and we subtract all the >numbers that end in 9 (i.e remove 1/9, 1/19, 1/29 etc) I was told >that the seresi still diverges, why? And fran...@math.ksu.edu (Francis Fung) replies: >... it is not too hard to see that in fact 1/9 + 1/19 +1/29 ... >diverges. Think of it as 1/10 (1/.9 + 1/1.9 + 1/2.9 +...) . Each >term inside is bigger than the corresponding term in the harmonic >series and so diverges. Quite true. >On the other hand, convergence of what's left over is not entirely >obvious and is a fairly interesting thing to prove. It basically >depends on estimating what's left over by grouping the terms by >the number of digits in the denominators. For all of this stuff >I suggest the excellent book "Ingenuity in Mathematics" by Ross >Honsberger, Math. Assc. of America press. Well, the exponential grouping method is how you show the harmonic series diverges in the first place, and it will work for any of this. But you can easily see that the harmonic series, omitting the reciprocals of numbers ending in 9, diverges. For instance this sum must include the reciprocals of numbers ending in 8, which can be shown to diverge just as you have shown above. > Please follow up to sci.math. Thanks! Well, this is pretty elementary for sci.math, so I wouldn't bother. I do, however, think it's time for Yossi to get a textbook. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Date: Wed, 08 Jan 92 21:20:01 -0500 (EST) From: Dan Hoey To: Cube Lovers Subject: Rubik's Cube, the minimax number of moves mkt@vax5.cit.cornell.edu (Gregory E. Dionne) asks: Does anybody know what the minimum number of moves are required to solve the 3x3 and/or 4x4 cubes in the worst-case scenario? and receives some answers, some of them accurate. The following is my understanding of the best answers now known, which I am sending both to rec.puzzles and the Cube-Lovers mailing list. The latter will, I hope, excuse some information repeated from the archives. First, you have to decide what you mean by a move. On grounds of symmetry and parsimony I prefer to count each quarter-turn of a face as a (QT) move. However, most of the literature counts either a quarter-turn or a half-turn of a face as a single (HT) move, and there has been more work done on the problem by the HT contingent. Second, you have to be careful to define what constitutes solved! While most people are content to make each face a solid color, some cubes have markings that display whether the face centers are twisted with respect to the rest of the cube. [This has recently been done commercially in an spectacularly braindamaged way, in a product known as ``Rubik's cube--the fourth dimension'' or some such nonsense. The mfrs have marked only four face centers, breaking symmetry while they fail to show the surprising invariant of the Supergroup. What bagbiters!] But that is a topic for other messages; I will not further discuss the invisible features of cubes here, save to note that there are more invisible features in larger cubes, and that if you take them into account, the cube will be harder to solve and require more moves than if you don't. Third, you have to understand that in either case, nobody knows the exact answer except for the tiny cubes. It boils down to knowing lower bounds L and upper bounds U, such that there must be some positions requiring at least L moves, while any position can be solved in at most U moves. I will discuss these in turn, below. For lower bounds, it is easy to calculate how many positions of Rubik's cube are achievable, and we may reason that only a few positions are within a few moves of start. Counting them, we can determine that at least 21 QT (or 18 HT) are needed to solve some positions of the cube. In fact, at least half of the positions of the cube require at least 18 HT, and at least 90% of the positions require at least 20 QT. The calculations are elementary, and have been known for over a decade. Nobody knows any other very good way of finding lower bounds. In Rubik's_Cubic_Compendium (1987), Tamas Varga writes Experts believe that even in the worst cases--the patterns furthest away from start--it should be possible to restore the cube in 20-odd [HT] moves, maybe 25, not more. However, such beliefs are clearly conjectural, based on the behavior of much simpler puzzles. The known upper bounds are constructive, consisting of a solution procedure guaranteed to solve any cube within U moves. The best known bound is embodied in a procedure invented by Morwen B. Thistlethwaite, and improved by students of Donald E. Knuth (The students are not identified in R_C_C). The improved procedure requires at most 50 HT in the worst case. Thistlethwaite was hoping (in 1980) to improve this to 41 HT, but (rumors to the contrary) he apparently did not succeed. A 1989 article by Hans Kloosterman entitled ``Rubik's Cube in 44 moves'' refers to an attempt to refine Thistlethwaite's method. I have not heard of any success there, either. Since any HT is at most 2QT, any Rubik's cube position can be solved in at most 100 QT using Thistlethwaite's method. According to my understanding of the method, this can actually be reduced to 97 QT, but this is still poor. A method tailored to minimizing QT would almost certainly guarantee a much shorter solution. Unfortunately, Thistlethwaite's method requires enormous tables of partial solution methods. Gerszon Keri describes a simpler method in R_C_C that requires at most 97 HT and which humans can memorize. The method is attributed to ``a Cambridge group,'' which I think must refer to England. According to Keri the Cambridge method has been refined to use only 79 HT, but I do not know if the refined version is still humanly comprehensible. For the 2x2x2 cube, the worst-case number of moves is known to be exactly 14 QT (11 HT). Only 276 (2644) positions require all 14 QT (11 HT). Half of the positions can be solved in 11 QT (9 HT) or fewer. For the 4x4x4 and larger cubes, the problem of defining a move is more complicated. Besides the QT/HT dichotomy, there is the question of whether a move consists of a slice (turning one part of the cube with respect to the other) or a slab (turning a 1x4x4 section of the cube with respect to the rest). We might expect that, as we do not count the center-slab moves of the 3x3x3 as a single move, we should not count the inner-slab moves of the 4x4x4 as a single move. However, I have discovered excellent reasons of symmetry (send email if you want to know) for us to consider all slabs alike, whether internal or face, with the exception of the center slab of an odd-sized cube. This is known as the Eccentric Slabist metric. According to my calculations of some years ago, some 4x4x4 positions require at least 37 slab QT or 41 slice QT to solve. The Eccentric Slabist also calculates at least 59, 81, 111, 138, 175, and 208 QT for the 5x5x5 through 10x10x10 cubes. (And yes, I've heard the widespread misinformation that Rubik's cubes larger than six cubies on an edge are impossible). I seem to recall calculating HT lower bounds, but I can't seem to find them. I do not recall whether upper bounds have been calculated for the large cubes, other than that they are O(N^2)--see J.A. Eidswick's article in the March 1986 Math Monthly. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: rec.puzzles From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 8 Jan 92 23:58:24 GMT Subject: Re: Noughts and crosses se...@fid.morgan.com (Seth Breidbart) writes: >The more interesting question is for a game of k in a row on an n x n >board. For what values of k and n is there a win? Is (the largest >such) k eventually constant or does it increase with n? Berlekamp, Conway, and Guy's _Winning_Ways_ reports proof that the maximum k is between 4 and 7 inclusive, and it appears to be 5 or 6. They report: . 4-in-a-row is a draw on a 5x5 board (C. Y. Lee), but not on a 4x30 board (C. Lustenberger). . N-in-a-row is shown to be a draw on a NxN board for N>4, using a general pairing technique devised by A. W. Hales and R. I. Jewett. . 9-in-a-row is a draw even on an infinite board, a 1954 result of H. O. Pollak and C. E. Shannon. . More recently, the pseudonymous group T. G. L. Zetters showed that 8-in-a-row is a draw on an infinite board, and have made some progress on showing infinite 7-in-a-row to be a draw. cos...@cosell.bbn.com (Bernie Cosell) writes: >Well, there is always go-moku, which is 5-in-a-row played on a 19x19 >go board. It is a known win for the first player, and so the >Japanese have introduced several 'handicaps' for the first player >[e.g., he must win with _exactly_ five: 6-in-a-row doesn't count], >but apparently the game is still a win for the first player. Apparently, yes, but I don't know if even the plain 5-in-a-row has been _proven_ to be a win, even on an infinite board. I haven't been through the _Winning_Ways_ bibliography yet, but I think they would have mentioned such a result. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: rec.puzzles From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 9 Jan 92 00:52:03 GMT Subject: Re: Perfect numbers (was 2 things...) c...@ra.msstate.edu (Charles Evans) asks: > P.S. is there any algorithm for finding perfect numbers, i...@prg.ox.ac.uk (Ian Collier) writes: > The algorithm as far as I know is just to factorise the numbers and > add the factors up.... No, you do much better forming the number out of prime powers. You still have to do some factoring, but of much smaller numbers, (p^a-1)/(p-1). Also, you never ``add the factors up,'' you use multiplicativity. > ...For example, if 2^k-1 is prime for some value of k Such values of 2^k-1 are called Mersenne primes. > ...Incidentally, the highest prime currently known is 2^k-1 for some > large k (five digits, starting with 6...). Wrong again. As of mid-1990, the known exponents of Mersenne primes were k=2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, and 216091. Any other Mersenne primes must have 150000350000. Perhaps you were remembering that 2^216091-1 has 65050 decimal digits. At any rate, the largest known prime is the 65087-digit non-Mersenne prime 391581*2^216193-1. As h...@nasa.nas.gov (Edward C. Hook) mentioned, any perfect number not of the form 2^(k-1)(2^k-1) must be odd, and is not known whether any exist. As of 1989 it is known that any such must be greater than 10^300. Thanks to Chip Kerchner and Bob Silverman for posting these status reports in 1990. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Date: Fri, 10 Jan 92 18:32:35 -0500 (EST) From: Dan Hoey To: Cube Lovers Subject: Re: Rubik's Cube, the minimax number of moves tjj@lemma.helsinki.fi (Timo Jokitalo) asks I wonder how large the necessary tables for Thistlethwaite's method for the cube are? I seem to recall reading that there were a few hundred entries.... Well, this is the information from Singmaster's _Notes_on_Rubik's_ _Magic_Cube_ (1980). Thistlethwaite's method is to work from group to subgroup as follows: G0: G1: G2: G3: G4: The following table shows the number of cosets (the index of each subgroup in the next larger group). Then I include the number of HT moves proven, anticipated, and best possible, from the 1980 N_o_R_M_C. Finally, I include the number of HT claimed in the 1987 R_C_C. It is interesting to note that the improvement did not occur where Thistlethwaite anticipated it. Step | Number of Cosets | Number of HT, 1980 | #HT, 1987 | | Proven Anticipated Best | Proven | | | 1 | G0:G1 = 2,048 | 7 7 7 | 7 2 | G1:G2 = 1,082,565 | 13 12 10 | 13 3 | G2:G3 = 663,552 | 15 14 ? 13 ? | 15 4 | G3:G4 = 29,400 | 17 17 15 ? | 15 -----+-------------------+-----------------------------+----------- Total HT | 52 50 ? 45 ? | 50 Total QT | 101 97 ? 87 ? | 97 I had thought the tables contained one entry for each coset, and so there would be over a million entries for step 2. However, I was surprised just now to notice in N_o_R_M_C that tables were only needed in step 4, and then only 172 entries, so there must be some abbreviation or algorithmic approach. Of course, when Knuth's students improved step 4, they may have changed it to use a huge lookup table; I don't know. Still, this is much better than the situation I expected in my note two days ago. In listing QT I assume that in we can require steps 1, 2, and 3 to each end with a quarter-turn. So the number of QT is at most three less than twice the number of HT. And, more important, have they been published, or does anyone have them in an electronic format? The bibliography in N_o_R_M_C mentions Thistlethwaite's algorithms as being in typescript, but I don't know if they were available by request, and I don't know anyone who has them. I don't know anything about the improvements by Knuth's students, and there's nothing in the R_C_C bibliography that looks like a Stanford tech report. Dan --- Newsgroups: alt.folklore.computers Date: 13 Jan 92 15:56:35 GMT From: hoey@aic.nrl.navy.mil To: Post-NetNews@ucbvax.berkeley.edu, Feature-Entenmanns@mc.lcs.mit.edu Subject: Re: Naming languages jn11+@andrew.cmu.edu (Joseph M. Newcomer) writes: > After the gross injustices done to Blaise Pascal and Ada Lovelace in > the name of "languages", I think the best way to honor Adm. Grace > Hopper is to vow to /not/ name any language after her. Good idea, but fortunately unnecessary. She is not subject to such mistreatment, having already given her name to a device for handling punched cards. Dan --- Date: Tue, 14 Jan 92 12:49:16 -0500 (EST) From: Dan Hoey To: Cube Lovers Subject: A new upper bound: 91 QT I just wrote a quick program to count the number of QT to move from the full cube group to the subgroup generated by . Thistlethwaite computed that this takes at least 7 HT in the worst case. The surprisingly good result is that it also takes only 7 *QT* in the worst case. This reduces the upper bound I posted Friday to 91 QT. I had wondered if the worst cases could be reduced by choosing a different pair of faces to restrict to half-twists. Unfortunately, the all-edges-flipped position is one of those that requires at least 7 HT (and so 7 QT), and by symmetry it cannot be improved. Allan C. Wechsler analyzed his own cube-solving method, finding that: For example, flipping two edges in place takes 22 qtw. This can be done in 16 QT, though I don't know if that is the best known. Any pair can be flipped with a conjugate of the 14 QT slice mono-op FOTAROFATO-RAM TAFORATOFA-ROM (FT'RF'T L'R B'TR'BT' LR'). Adjacent and antipodal pairs require the introduction of a non-cancelling QT in the conjugator. Obviously a lot could be gained from tweaking the earlier part of the algorithm to guarantee that I don't need to do this at the end. Probably, but it's hard to make that guarantee. The problem is that unless you flip edges in place with no other action (the very problem you're trying to avoid) you may affect the later choices in the algorithm, making the earlier tweaks wrong for that branch of the algorithm. For instance, the 7-QT method my program found solves the orientation of all the edges (using a particular non-standard labeling of the orientation that, when solved, is invariant under F^2, B^2, L, R, T, and D). But it may permute edges, and permute and twist corners, so it may not form a useful part of an arbitrary cube-solving algorithm. It works in Thistlethwaite's only because he is careful in all branches of the rest of the algorithm never to mix up the orientation of those edges. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: sci.misc From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 14 Jan 92 23:15:41 GMT Subject: Re: red LED vision lo...@APLPY.JHUAPL.EDU (Louis Vasquez) writes: >If I take my red led digital clock in a dark room, and shake >it. It appears that the digits move out of phase with the clock. I'm pretty sure this is an effect of the cones of your eye operating faster than the rods, but the cones see only the digits (since they need a lot of light). ga...@hpldsla.sid.hp.com (Gary Koerzendorfer) and orn...@kodak.kodak.com (Barry Ornitz) have both claimed this is a stroboscopic effect due to the rapid pulsation in most LED displays. I do not believe this can be true, because the same effect is visible with a burning ember moved back and forth in the dark. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: rec.humor From: hoey@ETL.ARMY.MIL (Dan Hoey) Date: 16 Jan 92 14:46:27 GMT Subject: Re: Palindromes : a compilation wo...@iear.arts.rpi.edu (Chris Widmann) writes: >Well, a year ago I started to collect palindromes from people on the net..... >Longer palindrome: >A man, a plan, a cat, a ham, a yak, a yam, a hat, a canal--Panama! That palindrome was written by Guy Jacobson, as I noted when I originally posted it some years ago. Please do not distribute it without attribution. >Longest palindrome: >A man, a plan, a caret, a ban, ..., a bater, a canal--Panama. It is not the longest palindrome on record. Also, I discovered it. Do not distribute it without my name. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: sci.physics From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 16 Jan 92 16:27:49 GMT Subject: Re: Residential Gas Meters m...@andante.att.com (Mark Cravatts) asks: >They measure in ccf. What unit of measure is this? bhoug...@pima.intel.com (Blair P. Houghton) answers: >Volume; one ccf is one hundred (c) cubic (c) feet (f). That should be hcf; ccf should be one one-hundredth. Or is our archaic measuring system making fun of us again? Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: sci.physics From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 16 Jan 92 16:39:51 GMT Subject: Re: Air density sh...@eos.arc.nasa.gov (Richard Barry Shrum) writes: >Does anyone have the answer to what the correlation of atmospheric >pressure (~14.7 psi sea level) is to air density? What is normal air >density on earth at sea level? acamp...@magnus.acs.ohio-state.edu (Angelo Campanella) replies: >Some simple facts: >1/ normal sealevel air density is 1.2 kg/cubic meter; you figure it out for >PCF, etc. I say a pound per cubic yard and let it go at that. Certainly you mean 2 lb/yd^3. Also, you'd better keep track of gas content. On hot, humid days the density decreases significantly due to water content. Significantly enough to impede aircraft takeoff, according to pilots. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: sci.physics From: hoey@ETL.ARMY.MIL (Dan Hoey) Date: 17 Jan 92 15:29:02 GMT Subject: Re: Air density (as related to humidity and temperature) pk...@andrew.cmu.edu (Paul Karol) writes: >In the comment about air density going up in warm humid air...how can >this occur for gases, as explicitly stated.... I don't know where you read that comment. The only message I find in sci.physics relating air density and humidity is my own, where I (explicitly) state: > ... On hot, humid days the density decreases significantly due to > water content. ^^^^^^^^^ Paul continues: >... the gas law for 1 atm says the density should drop at higher >temperatures and furthermore, replacing an average air molecule of >atomic mass ~29 with one of water of mass 18 (one-for-one replacement >to stay at atmospheric pressure) should also lighten the load? Yes, though I think the decrease due to the gas law is inconsequen- tial. More critical is the increase in water vapor pressure, which implies a greater water content per relative humidity. Right? You're the chemist, I'm just remembering high-school physics and a chance conversation with a pilot. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: rec.humor.d From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 17 Jan 92 17:32:04 GMT Subject: Re: Palindromes : a compilation I wrote: >>>A man, a plan, a caret, a ban, ..., a bater, a canal--Panama. >>It is not the longest palindrome on record. Also, I discovered it. >>Do not distribute it without my name. a...@nelson.questar.mn.org (Alan L. Nelson) replies: >Hey, wait a minute. This WHOLE article was posted back in 1990 by my >best friend, Billy-Bob "Bubba" Kornschucker. >Please don't post this again without giving the correct attribution, I hope Mr. Nelson thinks he is quite funny; I hope so because that is preferable to his being a liar. But just so there is no confusion, I found that palindrome in 1984. I don't know of any Usenet appearance before I posted it in May, 1990. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: sci.crypt From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 23 Jan 92 15:19:02 GMT Subject: Re: 4 byte signature??? jmou...@cs.cmu.edu (John Mount) writes: >What??? 4 byte signature- that is only 2^(4*8) = 4294967296 values.... >So unless your application changes authentication keys every couple >of hours it can be spoofed. If you want a longer signature, you should be able to get it by appending the short signature to the message and generating a new short signature. Repeat to taste. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: misc.legal.computing, sci.crypt Followup-To: misc.legal.computing From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 28 Jan 92 19:54:38 GMT Subject: Re: PKP food generator brns...@nyu.edu (Dan Bernstein) writes: >... if an outside organization generates a key for you, it could >easily introduce (e.g.) a trapdoor based on the number field >sieve---e.g., RSA Inc. could generate RSA keys which had no obvious >weaknesses but could be broken in a few months without much computing >power. I am not so confident as others seem to be that this can be >detected..... The issue is moot, since they could much more easily keep a record of every key they generate. Not only could they ``break'' your key immediately, no one else could break it or detect its weakness without their cooperation. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: misc.misc From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 29 Jan 92 17:56:13 GMT Subject: Re: $1.00 word sstev...@oregon.uoregon.edu (Shirien Stevens) writes: > I know parents aren't supposed to be too helpful with homework, > but darn it, when your 11 year old spend two hours on a > mathproblem and still can't get it, it's time for me to jump in.... schum...@convex.com (Richard A. Schumacher) remarks: >This was given as MATH homework? The inquisitor, er, "teacher" >responsible should be shot. It depends on what the teacher is testing. It seems to be an effective test to find out which kids do their own homework and which ones farm it out to their parents, or the net. I should think an answer like ``I tried ten words and didn't come close'' scores higher than a list of two hundred words you got from someone else. And if some students hand in someone else's word list as their own work, it's a wonderful opportunity for introducing them to concepts of ethics and plagiarism. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: sci.crypt From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 30 Jan 92 22:49:41 GMT Subject: Re: 4 byte signature??? With regards to extending a four-byte signature I wrote: >If you want a longer signature, you should be able to get it by >appending the short signature to the message and generating a new >short signature. Repeat to taste. ghunt...@Reed.Edu (Galen Huntington) objects: >The entire point of having a signature is to prevent other >people from forging your mail. So someone else does a brute-force >search and produces a four-byte key. They can then send that out. >You can make your own signature as long as you like; that won't stop >other people. >What is needed is a standard length beyond which a signature >is legal. Which amounts to legislating a length, which is the same >problem there was with DES. I should hope any such standard would take into account how much is at stake and what the state of the art is. But that issue is different, and orthogonal from the algorithm we use to generate the signature of whatever length. It only points out how much we need the algorithm to be able to accomodate a variety of lengths. My point is that it is better to have an algorithm that generates a short signature, so you can specify the level of security needed with fine granularity. j...@osc.COM (Joe Keane) writes: :Re-scanning the message also means that you can't implement your :algorithm as a filter. You have to store the whole message :somewhere. Well, if the original algorithm was a filter, then you checkpoint it just before it reads the EOF, then repeatedly { feed it the EOF, get four bytes of signature out, restart from the checkpoint, feed it the four bytes, and recheckpoint }. But it's true this is a fairly lame way of extracting the large amount of internal state from the algorithm, if it has it. And if the state is not large, this scheme does not buy extra security. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: sci.crypt From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 1 Feb 92 01:42:28 GMT Subject: Re: Determining RSA private key given blackbox I believe there is a result that shows RSA to be insecure if you have the public encryption algorithm and a black box for decrypting chosen ciphertexts (where you don't get to choose ciphertexts that have been output as the encryption of secret messages, of course). My recollection is that it appeared at the Foundations of Computer Science conference in 1982 or 1983, the one in Chicago. Unfortunately, I didn't understand it then, and I haven't figured it out since, and I can't locate the proceedings just now. I'm sure it was a much harder method than the one b...@CS.CMU.EDU (Bennet Yee) posted, which seems to be flawed. It was probably a randomized attack, and had something to do with navigating sawtoothed functions. If someone knows about the paper, like whether it has been refuted or improved, I'd appreciate it if you'd drop me a line. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: sci.math Followup-To: poster From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 11 Feb 92 16:39:10 GMT Subject: R E B U K E to the Perpetrator of the Fermat's Last Theorem Poll I protest Gautam Dalmia's abuse of the sci.math newsgroup for his opinion poll. This amateurish experiment in amateur sociology has no relevance to mathematics. I condemn Dalmia's scurrilous slander of the motives of persons who abstained from his poll. I made it clear in private mail to him that would not take part because he was apparently planning to use the poll's results to support unjustified conclusions. His speculation that people did not respond for fear that they would be named is a transparent fraud. I would normally address the technical assertions that Dalmia makes with regard to Fermat's Conjecture, but I have no desire to assist in modifying his arguments to make their ridiculousness less patent. He is a crank, and ignorant cranks are at least easier to ignore. I will not dignify Gautam Dalmia's misbehavior with further discussion in this forum. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: sci.math From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 12 Feb 92 02:39:23 GMT Subject: Re: Two squares and NP-completeness ram...@unixg.ubc.ca (Keith Ramsay) writes: >(Robert D. Silverman) writes: >>Thus, your problem comes down to factoring b^2-a^2-c. >...with requisite bounds on the factors. The size of the number to be factored is at most twice the size of b, so that is not relevant to the NP-completeness. In order to make it an NP problem (rather than a #P problem) we impose a bound on the factor, but that is a technicality. >Is it known that the existence of a factorization (with a bound on >the factor) is not NP-complete? ... Strictly speaking, I believe for >anything in NP not to be NP-complete we need that P<>NP. For this reason, the question you are trying to ask is stated, ``Is a polynomial time factoring algorithm known?'' The answer is no, barring paranoid fantasies involving the NSA. (Though by branding them paranoid I do not mean to deny their possibility.) Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: rec.puzzles From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 12 Feb 92 23:49:50 GMT Subject: Re: "the other is a girl" - a chance to read the rules bri...@bari.Eng.Sun.COM (Brian Gordon) writes: >...For the nonbelievers, here is a chance to take $10,000 cash from >me by taking advantage of my stupid insistence on 1/3 as the answer. >Here is an equivalent problem that is easy to duplicate: we'll flip >two coins and take the cases where at least one of them is a HEAD, ^^^ ^^^^^ >and bet on the likelihood that the other is too. You're playing a different game. Let's play the coin game with the same rules as the offspring game. We'll get someone else to flip two coins, and occasionally she will tell you (truthfully) that one of them is a head. What's the probability that the other is a head THEN? Based on how she decides, it can be anywhere from zero to one. Note that she is not required to tell you anything every time she flips the coin, any more than women are required to walk up to you at parties and start discussing the sex of their offspring. >P.S. Nobody ever took me up on playing the Monty Hall problem for >cash. The 50/50 crowd can still take me for $10,000 there, too. You probably expected Monty to offer you a chance to switch each time, too. If you don't change the rules in that game, Monty can keep you down to one win in three, and then only if you never switch. He does this by never offering to let you switch if it will help you. It's a fairly interesting problem, though of course overdone to death in this group. I don't find that your repeated ``offers'' to play a different game for money add anything, though. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: rec.games.go, rec.puzzles Followup-To: rec.puzzles From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 26 Feb 92 16:38:18 GMT Subject: Re: Go-moku (renju) book. In rec.games.go, w...@math.canterbury.ac.nz (Bill Taylor) writes about the book > FIVE-IN-A-ROW (RENJU) > For beginners to Advanced Players > by Goro Sakata 8-dan and Wataru Ikawa 5-dan > Ishi Press - Tokyo - 1981 and their attempt to demonstrate that unrestricted five-in-a-row is a first player win on a 15 x 15 board. I do not believe this has been proven, even for an infinite board. >OPEN CHALLENGE TO ISHI PRESS. >If the authors have discovered a detailed proof of unrestricted black >win, as they seem to claim, it should be possible to program it >without too much difficulty. Such a program could easily be emailed >to western go/gomoku and computer people, for independent verification. The challenge is too strong, for they could conceivably develop a nonconstructive proof, or at least a proof that does not yield a tractable algorithm for play. I think this is the current status of Hex, for example, or at least of Hex generalized to a large board. The challenge is also too weak, for a program that no one knows how to beat does not constitute a proof that it is unbeatable, or that an unbeatable one exists. Unfortunately, I doubt that the authors are interested in considering the deficiencies of their demonstration from a mathematical standpoint. People who play games professionally tend to believe they have demonstrated any number of things, and they are too used to dealing with nonprofessionals who cannot fill in the trivial gaps of a proof in their specialty to believe one who points out a nontrivial gap. It isn't restricted to the Japanese, either. Try talking to a chess master about the possibility that White is in zugzwang on move 1, and must lose with correct play. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: comp.ai Followup-To: poster From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 4 Mar 92 19:19:48 GMT Subject: Call for papers: Biases in Inductive Learning I've been asked to forward this call for papers / participation to the newsgroup. Note that replies should be sent to gor...@AIC.NRL.Navy.Mil (Diana Gordon), who has no access to comp.ai, and that the deadline for preliminary versions is March 12. ==================================================================== CALL FOR PAPERS Informal Workshop on ``Biases in Inductive Learning" To be held after the 1992 Machine Learning Conference Saturday, July 4, 1992 Aberdeen, Scotland All aspects of an inductive learning system can bias the learn- ing process. Researchers to date have studied various biases in inductive learning such as algorithms, representations, background knowledge, and instance orders. The focus of this workshop is not to examine these biases in isolation. Instead, this workshop will examine how these biases influence each other and how they influence learning performance. For example, how can active selection of instances in concept learning influence PAC convergence? How might a domain theory affect an inductive learning algorithm? How does the choice of representational bias in a learner influence its algo- rithmic bias and vice versa? The purpose of this workshop is to draw researchers from diverse areas to discuss the issue of biases in inductive learning. The workshop topic is a unifying theme for researchers working in the areas of reformulation, constructive induction, inverse resolu- tion, PAC learning, EBL-SBL learning, and other areas. This workshop does not encourage papers describing system comparisons. Instead, the workshop encourages papers on the following topics: - Empirical and analytical studies comparing different biases in inductive learning and their quantitative and qualitative influ- ence on each other or on learning performance - Studies of methods for dynamically adjusting biases, with a focus on the impact of these adjustments on other biases and on learning performance - Analyses of why certain biases are more suitable for particular applications of inductive learning - Issues that arise when integrating new biases into an existing inductive learning system - Theory of inductive bias Please send 4 hard copies of a paper (10-15 double-spaced pages, 12-point font) or (if you wish to attend, but not present a paper) a description of your current research to: Diana Gordon Naval Research Laboratory, Code 5510 4555 Overlook Ave. S.W. Washington, D.C. 20375-5000 USA Email submissions to gor...@aic.nrl.navy.mil are also acceptable, but they must be in PostScript. FAX submissions will not be accepted. If you have any questions about the workshop, please send email to Diana Gordon at gor...@aic.nrl.navy.mil or call 202-767- 2686. Also, please note that I am unable to read messages posted to this newsgroup, so replies to this announcement should be sent via email only. Important Dates: March 12 - Papers and research descriptions due May 1 - Acceptance notification June 1 - Final version of papers due Program Committee: Diana Gordon, Naval Research Laboratory Dennis Kibler, University of California at Irvine Larry Rendell, University of Illinois Jude Shavlik, University of Wisconsin William Spears, Naval Research Laboratory Devika Subramanian, Cornell University Paul Vitanyi, CWI and University of Amsterdam ==================================================================== Please reply to gor...@AIC.NRL.Navy.Mil (Diana Gordon). Dan Hoey --- Newsgroups: rec.arts.books From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 9 Mar 92 14:52:26 GMT Subject: Re: Drowning by Numbers (minor, veiled spoilers) hoey@AIC.NRL.NAVY.MIL (I) wrote: >On the way out the door, Cissie 1 ... empties a pocketful >of gravel on the dressing-table. ``It's your gravel.'' > Cissie 2: Thank you, Mother, you might have emptied it outside > where it belongs. > Cissie 1: Well--you know--Virginia Woolf. Thanks to Mark Taranto, Barbara Hlavin, Robin Boswell, and Kate McDonnell, all of whom informed me that Virginia Woolf drowned herself after putting rocks in her pockets to weigh herself down. C1 is presumably making the point that where the gravel belongs depends on what you intend to do with it. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: sci.math From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 12 Mar 92 19:16:05 GMT Subject: Re: Special points inside triangles so...@swifty.dap.CSIRO.AU (Peter Somlo) writes: >> we have proposed a statistically probable point for which the sum >> of the squared distances to the sides is a minimum. This point is >> also the point which results by shrinking the triangle in a >> proportional manner down to a point. w...@math.canterbury.ac.nz (Bill Taylor) replies: >Actually this "proportional shrinking" is not quite unambiguously >defined here... Well, that's putting it mildly. In fact, you can pick _any_ point in the triangle as a fixed point as you shrink the triangle proportionally. You could even pick a point _outside_ of the triangle. Whatever fixed point you choose will be the limit of the shrinking triangles. By assuming the sides move at an equal rate, Bill shows that the limit is the incenter. We could instead require the vertices to move at an equal rate, in which case the limit would be the circumcenter. So we must ignore the ``proportional shrinking'' remark and pick the point that minimizes the sum of the squared distances. David Joyce did this quite expertly in his message . >I hadn't realized it also minimized the sum-of-distance-squares.... It doesn't. Dan --- Newsgroups: comp.programming From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 18 Mar 92 23:47:17 GMT Subject: Re: Hashing strings raghu@vnet.ibm.com writes: > A recent paper has a catalog of hashing functions. >... > B.J. McKenzie, R.Harries, and T. Bell, "Selecting a Hashing > Algorithm", Software - Practice and Experience Vol. 20(2), > Feb. 1990, pp 209-224 >... I hope they note the drawbacks of the methods they list, where (on machines with the popular sizeof(unsigned)==4): gnucpp's hash function ignores all but the last 16 characters of the string, the hash functions of pcc, cpp, and c++ ignore all but the last 32 characters of the string, and icon's hash function ignores the order of characters within a string. These problems aren't so harmful in C, since its paralyzed macro processor (and in some implementations, few significant characters in identifiers) militate against the long, uniform identifiers often created by code-generating tools. But I've seen such code incorporated into Lisp interpreters, where it can bring some programs to their knees. Don't do that. Dan Hoey@AIC.NRL.Navy.Mil --- Newsgroups: comp.arch From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 24 Mar 92 22:36:25 GMT Subject: Re: Standard term for bit ordering bran...@inf.ethz.ch (Marc Brandis) writes: >I ran into the problem of finding an appropriate term for the bit ordering >of different architectures. While big-endian and little-endian are common >terms to refer to different byte-orderings, I am not sure on whether this is >also widely understood for bit-orderings. As I recall the defining document--``On Holy Wars and a Plea for Peace'' or something like that--the terms were most emphatically used to refer both to bit orderings and to byte orderings, as well as to orderings of any other addressable unit. In the case of some machines, the bit-addressability is not obvious, but there is usually some instruction or another that associates numbers with bit positions. And I would not completely discount the ordering imposed by the plans and documentation. If they impose a numbering scheme, that is an endianness, and it may or may not agree with the endianness implicit in various architectural features. It is possible to write accurate documentation whose endianness conflicts with the architecture, it just is messier and harder to understand. The terms ``big-endian'' and ``little-endian'' are an extension of the more traditional terms ``MSB-first'' and ``LSB-first''. ``First'' usually refers to the order imposed by the addressing system in use, though it often referred to the time order of some bit-serial transmission technique. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: rec.puzzles From: hoey@AIC.NRL.NAVY.MIL (Dan Hoey) Date: 27 Mar 92 16:00:05 GMT Subject: Re: (different) Number puzzle sstra...@hopi.intel.com (Stephen Strazdus) incorrectly answered a puzzle: > It is the only 10 digit number containing all 10 digits, that is evenly > divisible by any single-digit number. I would ask how many 10 digit numbers there are with this property, assuming we don't count zero as a single-digit number. I have only been able to produce a heuristic argument that the number is fvk snpgbevny gvzrf fvkgrra. I'd like to see a concise rigorous argument, or barring that, confirmation by computer search. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: comp.lang.c, comp.theory Followup-To: comp.lang.c From: hoey@AIC.NRL.NAVY.MIL (Dan Hoey) Date: 27 Mar 92 17:08:24 GMT Subject: Re: How can you get `x % 3' without division k...@tfd.COM (Kent Hauser) writes: >Is there a way to generate x mod 3 (or x div 3) without performing >a divide? I need to do *lots* of them & my machine is much better >at shifting & adding. >For what it's worth, the input is a 14 bit unsigned number, so >loss of precision on overflow is not a problem. As far as computing the modulus goes, a variant of the method b...@gauss.mitre.org (Robert D. Silverman) proposed is to note that the we can treat the 14-bit number as a seven-digit number in base 4. Then we just cast out threes. int mod3( unsigned x ) /* x <= 16383 */ { static int m3tab[11]={0,1,2,0,1,2,0,1,2,0,1}; x = (x >> 6) + (x & 63); /* x <= 318 */ x = (x >> 4) + (x & 15); /* x <= 33 */ return m3tab[(x >> 2) + (x & 3)]; /* index <= 10 */ } Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Date: 27 Mar 92 21:28:24 GMT From: hoey@aic.nrl.navy.mil (Dan Hoey) Reply-to: sf-lovers-written@Rutgers.Edu Subject: Daniel Pinkwater sighting At Lunacon last weekend I was privileged to see an interview with Daniel Pinkwater, author of a number of odd tales for children, young adults, and childish geezers like me. He apparently never goes to conventions, but someone managed to offer him something he couldn't refuse, I forget what. But since if you missed it, you probably won't get to see him ever again, I'll try to remember what I can. He looks like he describes himself: very round, kind of like the pictures on Fat_Men_From_Space, if I remember them right. He's not quite as spherical as the life-size statue in the photo on the back of Alan_Mendelsohn,_The_Boy_From_Mars, but close. He told us the story of that statue. The book marketers made several copies (``I wish they had told me what they were planning to pay for it. I would have liked to make a bid.'' [paraphrased from DMP]) and distributed them to high-selling bookstores, and by raffle, and gave a few to Pinkwater to dispose of. He had a very active fan club at a high school in Ohio, so he sent one to its president. It didn't arrive, and didn't arrive; apparently the whole high school was beginning to turn against him because he wasn't delivering on his promise. So he tracked it through the shipper, and there was this signature that nobody at the school recognized. Somehow they checked through the school board files and found out that the person with the signature used to be a custodian at a different school in the district. Eventually they noticed that a teacher at the different school had the same name as the president of the fan club, so when the statue had arrived at HS A addressed to this guy, they'd said, oops, send it over to HS B. The teacher at HS B got this statue in the mail and thought ``Hmm, I know that guy,'' but couldn't place him. So he put the statue in his office, and waited for the guy who sent it to come by, and every day when he came in he'd think, ``Hmm, I know that guy.'' When they straightened it out, the teacher had become so attached to it he tried to get them to loan him the statue on weekends. Pinkwater decided there's something unsavory about this, and has advised them not to lend the statue. Asked what of his writing he liked best, he said it all needed rewriting, so he would rather it all be chucked. But when asked about the ``Norb'' comic strip, he changed his mind, and said that strip was good. Nobody understood it though, it was supposed to be a strip from the Golden Age of comics, where the strip told a story instead of just making a joke every day. People kept thinking they just didn't get it, though. It ended after a year, though the strips have been collected in an edition published by Miscellany Unlimited. Someone asked about the features he keeps using, like avocados and raisin toast. The answer was something like ``all the classic literature of the Western world uses avocados and raisin toast.'' Everyone thinks his name is a pseudonym. He said it isn't. Asked if it had been changed, he said yes, but the old name meant something equally strange in the old language. He wouldn't elaborate. Anne Werkheiser thinks it came from one of those movements to suppress the Jews in centuries past, where they made them all take funny names (She learned this from a Biology professor at USC, who made a study of these names, motivated by her own name: Katzenellenbogen, German for cats' elbows.) so they wouldn't be mistaken for Christians. It's sort of the inverse of Magyarization, where they made all the Jews take Hungarian names so they wouldn't stand out. But I digress... He ended up by reading his favorite story from Fish_Whistle, the story called ``Play it Again, Wolfgang.'' He had to hunt for it, because he could never remember the titles he gave to the pieces. It was the one about the hipster couple in the inner city, and the smarmy DJ who played his request as a seduction aid. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Date: 30 Mar 92 03:17:03 GMT From: hoey@aic.nrl.navy.mil Reply-to: sf-lovers-written@Rutgers.Edu Subject: Re: Daniel Pinkwater sighting CRAIG@MITVMA.MIT.EDU (Ed Craig) writes: >Nice to know Mr. Pinkwater's writing is appreciated. I wasn't sure what he >wrote. Well, if you read this on sflovers, maybe you'd be interested in his science fiction. For instance, _Borgel_ is definitely in the genre, though you'll find it in the ``young adult hardcover fiction'' rack, at least at Borders. It concerns an investigation into the nature of time, space, and the other. _The_Snarkout_Boys_and_the_Avocado_of_Doom_ is more of the action-thriller kind of story, but it does feature a living, thinking, computer built out of a giant avocado (which also makes a tasty salad) which I think qualifies as SF. It's in paperback. _The_Snarkout_Boys_and_the_Baconburg_Horror_ is more of a classic horror story. So, I hear is _Wempires_, which has aroused some fundamentalist bookburners who think it is soft on the undead. But _Lizard_Music_ is definitely SF. So is _Fat_Men_From_Space_. I would have to guess _Alan_Mendelsohn,_The_Boy_From_Mars_ is SF, though I haven't found a copy. Even his non-SF stuff is, well, weird. In _The_Wuggie_Norple_Story_, for instance, you have a horse (or was it one of the other pets) named Exploding Poptart. _The_Hoboken_Chicken_Emergency_ might be SF of the ``mad scientist creates monster that ravages city'' genre, except that it's mostly one of those touching stories about a boy and his giant chicken. The reason you don't see this more often is it's all on the YA racks, or in some cases in the children's section. Also it sells out in about two nanoseconds when people find out about it. So don't tell anyone, ok? Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: talk.bizarre From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 31 Mar 92 17:55:11 GMT Subject: Re: The Temptation of Saint Anthony klu...@grissom.larc.nasa.gov ( Scott Dorsey) writes: >phi...@solitary.Stanford.EDU (Geoff Phipps) writes: >>m...@saul.cis.upenn.edu (J. Oglethorpe) writes: >>>...`long pig'. >>That should be "longpela pik". >>"long pik" means " the pig". >Strange... in Dutch, "pik" is the polite, approved word for the penis. That's why the Water-Pik is marketed under the Dutch trade name "Wachstadtpol". Dan --- Newsgroups: misc.misc, talk.politics.misc, soc.culture.canada From: hoey@TEC.ARMY.MIL (Dan Hoey) Date: 31 Mar 92 18:09:11 GMT Subject: Adage (was Re: The Journal on 'Untying the Knot') scham...@watserv1.waterloo.edu (CHAMBERLAND S - BIOLOGY) digresses: > "Chat echaude craint l'eau froide". > (What's the equivalent in English?) ``Letting `I dare not' wait upon `I will.' '' You could look it up. Dan --- Newsgroups: comp.dcom.telecom From: Hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 10 Apr 92 22:19:41 GMT Subject: The Term `Bug' Originated With Edison In Telecom Digest v12n303 PAT notes: > [...Seriously though, the term 'bug' as used in software programming > does come from the late 1940's when the old vacuum tube style > computers had large relays in them into which insects would crawl to > hide; wind up getting squashed and cause the relays to malfunction. PAT] The term `bug' for a malfunction of electronic equipment dates back to the 19th century: Thomas Edison used the term with respect to telegraphy. PAT seems to have gotten a garbled version of the story in which a technician at the Mark I project taped a relay-raddled moth into a log book; he punningly labeled it the ``first actual bug found.'' Admiral Grace Hopper, who also worked on the Mark I, liked to tell the story accurately, but less-careful reporters have distorted it into a story of the origin of the term, even crediting her with the coinage. I understand she specifically denied that rumor in a recorded interview, which was rebroadcast on NPR shortly after her death. If anyone can provide more specific information about the interview or the rebroadcast, please email it to me. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: comp.dcom.telecom From: Hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 13 Apr 92 20:39:55 GMT Subject: Etymology of `Bug' and Bugs of Etymology In TELECOM Digest v12n311 I wrote: > The term `bug' for a malfunction of electronic equipment dates back > to the 19th century: Thomas Edison used the term with respect to > telegraphy. Which led our esteemed moderator to change the subject of my message from ``The term `Bug' '' to ``The term `Bug' originated with Edison''. But the latter statement is not what I meant. I don't know that the usage originated with Edison. For all I know, the usage of `bug' to mean a flaw in design or construction may have preceded the 19th century. On the other hand, I don't know that Edison *didn't* invent the usage, either. I only mentioned Edison because his use of the term contradicts the etymology involving 20th century insects. I appreciate PAT's attempt to tweak up the subject, but I don't want to start another bogus bug story. Let us instead take this as an example of how easily a minor misunderstanding can turn into a misleading assertion. Now can we get back to bugging the phones? Dan Hoey [Moderator's Note: Actually, your message arrived here with only the single word 'Bug' on the subject line ... not as you suggest, "The Term 'Bug'" ... and since one word subjects are not very descriptive and the gist of your message seemed to be that Edison was the first person using the term to the best of your knowledge, I thought that my line described the topic better than just 'Bug'. PAT] --- Newsgroups: news.misc, news.admin, misc.misc, news.groups Followup-To: news.misc From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 15 Apr 92 23:25:36 GMT Subject: Re: just what are those 40,000 hosts? (1/7) r...@pa.DEC.COM (Brian Reid) writes: >... So I decided to post some huge junk: the March 1992 list of hosts.... step...@sunlab.ka.sub.org (Stephan Niemz) responds: >Your file `allhosts.txt' contains 86098 lines, where the last >43049 lines are exactly the same as the first half! >Do you think your "information" is so important that everybody >has to see it twice? Perhaps Brian, or an unknown forger, noticed that at 7:18 GMT on the second of April the date was still 1 April in Palo Alto. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: rec.puzzles From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 22 Apr 92 22:31:45 GMT Subject: Representing 4 with 7's (was Re: hmmmm) Marc.Costa...@f2050.n391.z1.FidoNet.Org (Marc Costaldi) writes: >In this manner, can anybody express 4 in terms of three 7's????? dod...@convex.COM (Dave Dodson) answers: > +- -+ +- -+ > 4 = | (sqrt(77)/sqrt(7)) |, where | x | is the smallest integer = x. > | | | | Feh. If you're going to allow ceiling (aka smallest integer >=), then you only need _one_ 7 to make four. I think Knuth had the basic idea of how to do it. Four is the ceiling of the square root of the square root of the factorial of the square root of the ceiling of the square root of the square root of the factorial of the ceiling of the square root of the square root of the factorial of seven. I think it's conjectured that every integer greater than one can be represented with factorial, square root, ceiling, and just one seven (or any other number greater than two). As I recall, Knuth used floor instead of ceiling, and then you may be able to make all the positive integers. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: rec.puzzles From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 29 Apr 92 21:16:42 GMT Subject: Re: Counting down to 383, hints vt87...@cc.tut.fi (Timonen Vesa) asked: > Try to make 383 by using numbers: 1 2 25 50 75 100 > and operations: + - / * () Of course we are to use the numbers exactly once each, and it seems we must use the operators zero or more times each; one of the operators cannot be used nongratuitously. I'm surprised no one has gotten this one yet, since the solution is of a form that cuts down the search space quite a bit. For us brute-force hackers, it's an interesting experiment on the assumptions our code makes: Many programmers would code the search to *only* look at such expressions. On the other hand, some programmers may have made a different assumption, and ruled out the solution, which is unique up to commutativity. I made the assumption that the invisible operator is not allowed, and that division is exact; perhaps those have prevented me from seeing yet other solutions. I won't post the answer now. In fact, I'm concerned I might spoil someone's homework or contest or bar bet were I to do so. But if you write the expression in its most regular way, with no spaces and with traditional parenthesization, the /usr/5bin/sum program will fold it to '946 1'. Just so you know I got the answer. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: rec.puzzles From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 23 Apr 92 21:52:44 GMT Subject: Re: Rubik's Cube, Speed w...@math.canterbury.ac.nz (Bill Taylor) writes: > Well, believe it or not , I once did it in only 1.2 seconds, from a > completely random start ! > And I had a friend who claimed, (though there were no witnesses), to > have done it once in only 0.87 of a second !!!! I've always been concerned that ``random'' starts seem to have some small probability of turning out to be ``trivial'' starts. But there is a way of avoiding the worst of them. How many moves (quarter or half turns of a face) did you use? If it was fewer than seventeen moves, then the position you started from was one of the very easiest. It is easy to prove, using a counting argument, that such a position must be among the 4% of positions closest to start. I think such a result should be disregarded. I regret that I have no good way of determining ahead of time whether you are starting from a particularly easy position. Even afterwards, if you took seventeen or more moves, I can't prove it wasn't an easy position. But if you took fewer than seventeen moves you have demonstrated ipso facto that the position was an atypically easy one. Fortunately, if you are good at mixing up the cube, you won't have to throw out more than one trial in 28. It would be nice to figure out some way of preventing someone who got a too-easy position from inserting (F^2 B^2 L^2 R^2)^2 to add a fast gratuitous 8 moves. I guess I'll trust you not to pull that sort of rannygazoo. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: sci.math From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 1 May 92 19:16:54 GMT Subject: Re: rooks in d dimensions pr...@godel.mit.edu (Jim Propp) asked: > Given a d-dimensional chess board of size n, what is the smallest > number of rooks that can be placed on the board so that each of > the n^d cells is either covered or attacked? Someone wrote: >It is not clear to me what happens when n>=3 (what about just 3^3?). alope...@neumann.waterloo.edu (Alex Lopez-Ortiz), correcting for finger dyslexia (not dislexia), wrote: > This case is easy. Each rook covers at most 7 non-covered squares > since there are 27 squares the minimum number is ceil(27/7)=4. But that's not tight. Consider the least-populated of three parallel planes. All points not covered or attacked by a resident rook must be attacked by different nonresident rooks. Case 1: If there are no rooks resident, there must be 9 nonresident, so at least 9 over all. Case 2: If there is just one rook resident there must be four rooks nonresident, so at least five rooks on the cube. Case 3: If there are two or more rooks resident on the *least* populated plane, there must be six or more rooks on the cube. So there must be at least five rooks, and this is achievable using a straightforward floor(n/2)^2+ceiling(n/2)^2 upper bound construction. For general n^3, this says there must be at least max((n-k)^2+k,nk) rooks, for k the minimum plane population. This is tight for n<=4 and n=6 using the same upper bound, but in other cases there is a gap between the bounds. n lb ub 5 11 13 6 18 18 7 21 23 8 28 32 9 36 41 10 40 50 11 53 61 The lower bound is (3-sqrt(5))n^2/2+o(n^2) ~ .382n^2, while the upper bound is n^2/2+o(n^2). The technique can be generalized to yield a lower bound of max[0<=a<=d] min[0<=k<=n] max((n-k)^(d-a)+k,(n^a)k). Here k is the minimum rook population of n^a parallel hyperplanes of dimension d-a. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: rec.puzzles From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 5 May 92 12:35:23 GMT Subject: Re: Counting down to 383, spoiler With regard to making 383 out of 1,2,25,50,75,100 using +,-,*,/ d...@logos.wr.tek.com (Dan Tilque) writes: >The best I've been able to do on this puzzle is to get 384: >(50 - 2) * ((100 + 75)/25 + 1) You can get 383 with ((2+50)/25+1)*100+75. Of course, if you expect / as in C, the above expression is just 375. But then you can get 383 with (25*50-100)/(1+2). Pity there's no way to use the 75. If we had a language that rounded instead of truncating, we could use ((1+75+100)*50)/(25-2) or (2*75*(25+100))/(50-1). I imagine your problem lies in not dividing things that aren't divisible. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: alt.folklore.computers, alt.folklore.urban From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 5 May 92 23:10:32 GMT Subject: Re: gullibility tj...@JUTS.ccc.amdahl.com (Terry Carroll) writes: >There is no such word as "gullibility"; you don't believe me, then >look it up in the dictionary. s...@bristol.ac.uk (Paul Smee) writes: > Just did. axd7...@acfcluster.nyu.edu (Aaron Dickey) crows: > Uh, allow me to fill you in here. He got you to look it up. That > means you are gullible. Get it? Well, allow me to fill you in, too. He pretended not to have ever heard of this ancient chestnut, and got you to post an explanation of it. That means you.... Well, just a minute, allow me to fill me in here. He pretended to explain an ancient wheeze to an apparent gull, and got me to post an explanation of how, uh, I forget... ObUL: There's this guy out at a midwestern university who is amassing the worlds largest collection of punched cards. So if you're still hacking the dinosaurs, don't throw your dusty decks away.... ObCF: In 1977 I wrote some aircraft simulator diagnostics to run on a Harris minicomputer. I punched cards most every day. When I left that job, it never occurred to me I might not punch a card for over a decade. In 1989 I visited the computer museum and managed to coax a card out of their decrepit punch, and I imagine that may be the last I'll ever punch. Dan --- Newsgroups: alt.folklore.urban From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 5 May 92 23:29:42 GMT Subject: Re: gullibility a...@dayton.saic.com (Earle Ake) wrote: > My dad did something similar but with much better results.... The > idea was if someone were to hit the mailbox with enough force, the > mailbox would spin once around on it's base and strike whatever > might still be in it's way. > ....I wonder if anyone actually had the mailbox spin all the way > around and strike the car after hitting the mailbox. My dad did it slightly differently, such that the mailbox was on a reinforced arm extending at an angle toward the road. Top view: -------------------------------- car-> -------------------------------- Box \__ \__ \__ \__ \ pivot The idea is that if someone were to hit the mailbox from a car, the box would swing toward the car, catch the midsection of the person who hit it, and use the forward momentum of the car to push the head of the driver out the driver's side window, leaving most of the rest of the driver and passenger in the car. We were pretty sure they wouldn't try that trick twice. Since this was Texas, we thought that was a really good way of keeping people from messin' with our propitty. Of course, every now and then it snagged on the mailman's van when he drove by. Whooee, made one helluva mess. ObUL: Cattle mutilations are blamed on aliens to deflect suspicion from the real cause: farmhands who get a little rough when romancing their livestock lovers. You knew they couldn't be in it for the money. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: rec.puzzles From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 8 May 92 12:35:23 GMT Subject: Re: Triangle/Hexagon Area Ratio (corrected spoiler) If he spelled better, would have written: >From each vertex of an equilateral triangle draw two straight lines >to trisect the opposite side, defining an irregular hexagon in the >center. What is the area of the hexagon (as a percentage of the area >of the triangle)? torb...@diku.dk (Torben AEgidius Mogensen) wrote: > The ratio is 11/80. Which is not correct. Torben's mistake is in miscalculating the area of a triangle of base 1 and altitude sqrt(3)/10; he takes the area to be sqrt(3)/10. With this error corrected, Torben's method gets the right answer. I prefer a more geometric demonstration of the result, which I give below: In addition to drawing two lines from each vertex to trisect the opposite side, let us draw an altitude from each vertex to bisect the opposite side. The bisectors cut the central hexagon into six congruent triangular pieces. I will calculate the area of one of those pieces. Take such a piece that shares a side of the hexagon formed by a line from vertex A of the original triangle. The piece is the difference of two long triangles with vertex A, both of which have as sides: 1. the line from A to a point trisecting the opposite side, 2. the line from A to the midpoint of the opposite side, and 3. the altitude from a side adjacent to A. By the symmetry of the original triangle, there are just two kinds of such long triangles, and the difference of their areas will be the area of a sixth of the hexagon. Consider the ratio into which the triangle's altitude is cut by a line from a vertex to the opposite side B /|\ / | \E / |,'\ / ,'D \ / ,' | \ /,' | \ /______|______\ A H C The line AE has a vertical rise 1-BE/BC as far as that of AB, and covers a horizontal distance 1+BE/BC times as far as AB, so DH/BH=(1-BE/BC)/(1+BE/BC), and the area of triangle ADH is (1-BE/BC)/(1+BE/BC) times the area of triangle ABH, which is half of ABC. So as BE/BC assumes the values 1/3, 1/2, and 2/3, the area of ADH assumes the values 1/4, 1/6, and 1/10 the area of ABC. The two interior triangles with bases on BH then have areas 1/4-1/6=1/12 and 1/6-1/10=1/15 of the area of ABC. The difference of the two triangles is then 1/60 of ABC, so the hexagon has 1/10 of the area of ABC. The Egyptians would have loved this one. ObPuzzle: We stellate the hexagon in the diagram (extend its sides to get a skewed star of David). What is the star's area? What is the area of the two equilateral triangles of which it is the union? Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: rec.puzzles From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 8 May 92 14:49:12 GMT Subject: Re: Hypercube puzzle schni...@cs.ucf.edu (Mark Schnitzius) wrote: |> As you may or may not know, the largest area that |> a 1x1x1 cube can have, when projected onto a |> 2 dimensional plane, is sqrt(2) square units When I saw this claim, I thought it was quite strange that the maximum would be achieved in such a non-symmetric orientation, but I didn't get around to checking it. w...@math.canterbury.ac.nz (Bill Taylor) replied: > A cube can project a bigger area than that, as follows... > _________ > / \ \ > / \ \ > / \________\ > \ / / > \ / / > \ / / > ~--------' > ... giving A-max = sqrt(3) After seeing this, I verified that you can get the maximum area to be sqrt(3), and it's in exactly the configuration I expected. > Further calculation shows that, in the max configuration given above, the > projected cross-section is in fact a regular hexagon, side sqrt(2/3) Furthermore, the other two vertices map to the center of the hexagon. There was a discussion about the ``Halved Hypercube'' last month, and this is just the three-dimensional case. I suspect the answer to Mark's question is that you maximize the projected hyper-area by projecting two antipodal vertices together, yielding the same answer as the halved hypercube. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: alt.religion.kibology, comp.fonts Followup-To: alt.religion.kibology From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 8 May 92 15:33:32 GMT Subject: Proportional fonts (was Re: Kibo advocates killing of Microsoft) m...@central.cis.upenn.edu (Mr. Mung) wrote: > ...why not make ((4T+3H)/5), `seven fifths of the way from Times > Roman to Helvetica', a font that's even less like Helvetica, in a > Times-Roman-ish sort of way, than Times Roman is? You mean ((7T-2H)/5). ((4T+3H)/5) is three-sevenths of the way from Times Roman to Helvetica, and seven-fifths as fontly. Unfortunately, I suspect ``fontly'' just means ``big''. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Date: Tue, 12 May 92 11:03:34 -0400 (EDT) From: Dan Hoey To: Cube Lovers Subject: Diameter of the 2^3 cube and the 3^3 corners I sent the results of a quarter-turn analysis of these puzzles to Cube-Lovers in several messages during August, 1984. I modified a program written by Karl Dahlke to get these results. I counted both positions and local maxima at every distance up to the diameter of 14 quarter-turns. In case you don't have the archives handy, here are the results: Quarter 2^3 Puzzle Corners of 3^3 Puzzle Turns Positions Local Maxima Positions Local Maxima ____________________________________________________________ 0 1 0 1 0 1 6 0 12 0 _____2___________27________0______________114___________0___ 3 120 0 924 0 4 534 0 6539 0 _____5_________2256________0____________39528___________0___ 6 8969 0 199926 114 7 33058 16 806136 600 _____8_______114149_______53__________2761740_______17916___ 9 360508 260 8656152 10200 10 930588 1460 22334112 35040 ____11______1350852____34088_________32420448______818112___ 12 782536 402260 18780864 9654240 13 90280 88636 2166720 2127264 ____14__________276______276_____________6624________6624___ The first column agrees with Dik Winter's findings. As Michael Reid surmised, the diameters of the two groups are the same. My hazy recollection is that the 2^3 program ran for a few minutes on a Vax 750, while the corners program took a couple of hours. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: alt.folklore.urban From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 13 May 92 22:25:32 GMT Subject: Re: Arithmetic carrots d...@swindon.ingr.com (Desmond Mottram) writes: > Ask someone ten simple arithmetic questions, eg 3+5, 11-4, etc. Do > this quietly and seriously, then ask them to name a vegetable.... > The score for carrots beats all other vegetables about 60%-40%. > Why is this? > (You can tell posy or uncooperative b*****s because they will say > something like "globe artichoke"). I always used to answer ``Karen Ann Quinlan'' but I think she's shuffled off the mortal respirator. Do we have a new contender for canonical flatliner? (and no, I don't want to hear about your Uncle Frank, I'm looking for a *famous* gozer.) ObUL: The mentalist lobby made the government insert subliminal carrots into all the math lessons so this trick would work. Have you ever found yourself gnawing on a pencil while solving a hard problem? Now you know why! Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: alt.folklore.urban From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 14 May 92 11:52:38 GMT Subject: Re: Psych class urban legend? ccupp...@s.psych.uiuc.edu (Cyndi Cuppernell) writes: > Actually, though, whether it ever happened or not, I know some try > to do it. I work for a professor of psychology. He said he > recognized that one class he taught was trying to shape his > behavior, but he never figured out exactly what it was they were > trying to get him to do. When my psych class did that, we were trying to get the professor to believe we were shaping his behavior. He kept doing unusual things, trying to figure out what got the response. We had responses scheduled by the clock. Dan Hoey Hoey@AIC.NRL.Navy.Mil ObUL: Ad agencies drum up business by sticking secret messages in movies that say ``subliminal messages alter behavior.'' They have convinced a lot of people who are sure it's true but can't remember where they read it. --- Newsgroups: alt.folklore.urban From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 14 May 92 17:37:15 GMT Subject: Coverups (was Re: Apollo Mission Buzzed) lin...@positive.Eng.Sun.COM (Peter van der Linden) writes: > The standard response (which I do not find at all satisfactory) to > these kind of conspiracy theories is that all governments are > incapable of keeping anything secret for long, so they would certainly > be unable to maintain a conspiracy of silence about anything > interesting like unknown crafty aliens. [ numerous examples deleted ] The hard part (which is why it's so unsatisfactory) is figuring out whether information leaks are the exception or the rule. For instance, consider all the people it must have taken to fake the birth certificate, the pregnancy, the kid, the presidency (or to be precise, the first ladiency), the porn films, the telephoto nudes, and the fake Enquirer articles, and tell me how it never got out that Jackie is a man in disguise. Dan Hoey Hoey@AIC.NRL.Navy.Mil ObUL: The post office junks all the mail to Shergold; the news stories about sorting through it for bills are a CIA experiment in information control. --- Newsgroups: alt.folklore.urban From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 19 May 92 22:11:32 GMT Subject: Re: madonna is stinky mikkel...@thewav.enet.dec.com (snopes) writes: >... I've read plenty of articles ascribing such behavior to Madonna >that I wouldn't disbelieve the story out of hand, even if there were >no twists. I'm pretty sure all the Madonna stories have a twist. cra...@csd4.csd.uwm.edu (Craig R Albrechtson) > I heard a similar Madonna legend a little while back. According to > this particular Urban Legend, Madonna sometimes cruses the streets > of New York City looking for young males and when she sees one > she invites that person in for sex in her limo. Good luck kids. Just be sure to count your kidneys. ObUL: Young males go cruising New York City looking for Madonna intending to invite themselves into her limo. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: alt.folklore.urban From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 19 May 92 22:20:33 GMT Subject: Re: Drugged up cereal? With regard to LSD in breakfast cereal, kei...@hpdmd48.boi.hp.com (Keith Glasson) writes: > Sounds like Ul to me. Doesn't food have to be inspected? Well it's certainly a UL, but that doesn't mean it's impossible. The inspectors are looking for rat feces and mold. Of course, if they see some Blue Star(TM) tattoos they look a little harder. If someone actually did hallucinate after breakfast, they would look, and if there was LSD you wouldn't hear about it on AFU, you'd hear about it on every front page and radio talkshow. LSD is a much, much bigger audience attractor than cyanide. ObUL: Recent reports of contamination of Blue Diamond almond products with phosphorus from Blue Diamond matches have been hushed up by IBM and the big diamond interests. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: rec.puzzles From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 20 May 92 11:05:32 GMT Subject: Re: Solution of the Tiling Problem. ka...@top.cis.syr.edu (Kanad Chakraborty) writes about > tiling a 25 X 25 chessboard completely using only 3 X 3 and 2 X 2 > tiles.... My friend, L. Chandar solved the problem.... > A. Suppose that the rows of the board are labelled 1 through 25. > A 3 X 3 or 2 X 2 tile is said to `start' at row i, if it covers > rows i thru i+2 or i thru i+1 respectively.... That's the key insight! > There must be an even number (p') of 3 X 3 tiles starting at row 3. > This is because the 3 X 3 tiles starting at row 1 must END at > row 3, and there is an odd number (p) of such tiles at row 1.... Actually, this argument is wrong. We know an odd number of 3x3 tiles start at 1 and so end at 3. But that implies an odd number of 3x3 tiles starting at row 4, not row 3. But it's easy to repair the argument to prove that the number of 3x3 tiles starting at row i and ending at row i+2 will be odd if and only if i is congruent to 1 mod 3. Thus the number of tiles ending at row i will be odd exactly if and only if i is divisible by 3. This shows that the 25x25 board is not tileable with 2x2 and 3x3 tiles. In fact, it shows that for any MxN board to be tileable with 2x2 and 3x3 tiles, if M is odd then N must be divisible by 3. By symmetry, either 1. Both sides are even, or 2. Both sides are divisible by 3, or 3. One is neither, and the other is both. In this we can also disallow a side of unit length. It is easy to see by construction that these conditions are sufficient. ObPuzzle: What rectangles can be tiled with AxA and BxB tiles? Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: rec.puzzles From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 20 May 92 11:20:59 GMT Subject: Re: Pseudoshuffle With regard to shuffling a deck of cards by sequentially swapping each card with a random card, I wrote: > Well, for a two-card deck this provides a good shuffle. But for a > 3-card deck, you have a 14/27 chance, about 51.9%, of an even > permutation. The preponderance of even permutations continues to get > worse as the deck grows. At 52 cards you have a 56.5% chance chance > of an even permutation. The limit is (1+e^-2)/2, or about 56.8%. For odd-size decks, I got even and odd reversed. There is still a growing preponderance of one parity, but it is a preponderance of odd permutations in odd decks and of even permutations in even decks. warw...@cs.uq.oz.au (Warwick Allison) > The judges seem to be still out on this one (1 yea, 2 nay),.... The notion of reasoning by majority is ridiculous. > but how about this one ? (I used it in code, but now you've all got > me worried!)... > for each card in source deck > choose a number, I, between 0 and the size of destination deck > put card after the Ith card in the destination deck (where > "after the 0th" means "at the start"). If you are talking about starting with an empty destination deck and inserting the Nth card of the source by picking I from {0,1,...,N-1}, then that will work. It's just slower and harder to code than the usual correct method. The UCM is to shuffle in place by successiveley swapping the Nth card of the deck with the Ith card, for I picked from {1,...,N}. But if you are talking about shuffling in place by successively taking out the Nth card and putting it back into the deck after the I'th card, for I chosen from {0,...,TotalSize-1}, that does not yield a uniform distribution. I don't see a good way to calculate how far off it gets, though. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: rec.puzzles From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 20 May 92 11:43:25 GMT Subject: Re: Extension to Perfect Squares > I was fascinated with triplets (not the technical name I assure > you), that had the property: > x^2 + y^2 = z^2 They are called Pythagorean triples. > After a lot of work (oh, to have known more than geometry) I came up > with a simple formula to generate endless amounts of these triplets. When I was in high school I found the ones of the form (2n+1)^2 + (2n(n+1))^2 = (2n(n+1) + 1)^2 but as I learned later, these are only the skinniest ones. > However, finding the algorithm for squares should prove no problem here. Find it in any introduction to number theory. It's in the rubber bible, too, but I don't think they tell you why. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: rec.puzzles From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 20 May 92 11:57:16 GMT Subject: Re: Massive logic problem (FAQ, continued) cdmi...@cs.utexas.edu (Clinton Dean Mills) writes: > [ sum and product logic puzzle ] In particular, he posed the S&P puzzle for 2 <= x,y <= 99. ch...@peregrine.peregrine.com (Chris Cole) writes: > This puzzle is on the rec.puzzles FAQL (Frequently Asked Questions List). > S knows the sum x+y, P knows the product x*y, and they say the following: Hold it. The problem statement is still incomplete. S and P are also are presumed in this case to know that x and y are in [2,99]. (There are related puzzles in which and y have different bounds, and there are unbounded puzzles and puzzles where the numbers have lower bounds only.) We should also specify whether we (and more importantly, Messrs S and P) are to understand that x and y are distinct or not. Trying to go ahead and solve the puzzle without defining it is an invitation to forgetting the conditions. > P: I cannot determine x and y. > Product cannot be of the form a*b (both a,b prime), a*a = a^2, a*a^2 > = a^3, a*a^3 = a^4 (assume integers are not the same). Besides the assumption of distinctness, this uses the assumption that the lower bound on x and y is at least 2. Later, when the lower bound is relaxed, these conditions do not hold. > S: I knew you couldn't before you told me. > Since S *knew* this fact, he must have had a special sum S. Consider > the sets A(S), of all unordered pairs of integers (x,y) where S=x+y, > e.g. A(10) = {(2,8),(3,7),(4,6),(5,5)}. Remember to exclude x=y from this analysis. > Because of P's stmt, no pair > can be a prime pair (a,b) or a pair of the form (a,a^2) or (a,a^3). > The first integer that satisfies this condition is S=11 with A(11) = > {(2,9),(3,8),(4,7),(5,6)}.... > The next few S's and sets A(S) are: > A(17)=... > A(53)={...} > etc. I make A(53) to be the last element, at least for the [2,94] problem through the [2,105] problem. > The unique solution for the [2,100] case is: > SUM PRODUCT X Y > 17 52 4 13 As it is for every [2,N] with 62<=N<=400. There are no solutions for N<62. I don't know what the solutions are for larger N, or if the trend continues, but I fear it may require Goldbach's conjecture or something equally horrific. > The four solutions for the [1,100] case are: > SUM PRODUCT X Y > 5 4 1 4 > 9 8 1 8 > 15 56 7 8 > 19 88 8 11 You have apparently started to allow x=y here. Otherwise how could the product be 4 and P not know the numbers? > Halperin (IBM) and Moses (Stanford) have been using a similar puzzle > (variously called "the cheating wives" and "the dirty children") in > their recent work. The cheating wives problem is related only in that it also deals with public and private information. I would hardly call it similar. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: comp.misc From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 3 Jun 92 20:13:15 GMT Subject: What's `on' the internet (Re: oh no not again...) pe...@ferranti.com (Peter da Silva) writes: >My home system, taronga.com, has an MX pointing to the University of >Houston. I can send and recieve mail and news, but I am NOT on the >internet. I do not have any real-time access to network >applications, only a batch queue .... The most common term for this is that you are on the `internet' but not on the `Internet'. The upper-case Internet refers to systems connected by the IP protocols to the nsfnet/milnet core. The lower- case internet is a superset consisting of the systems that can exchange mail with the core. Sometimes the latter is restricted to systems that have a domain name recognized through an MX or A record, as opposed to those that require some sort of !::% routing. >On the other hand, neosoft.com is MXed at PSI, but it also has >real-time access to TCP applications (FTP, TELNET, IRC, etc...) via a >dialup link to PSInet. I would say the PSInet dialup is on the Internet, not neosoft.com. Neosoft is only on the internet. >Looking at nameservers does not tell you one way or the other whether >a system is effectively on the Internet. Actually, you can pretty much equate the Internet to those systems with `A' records, and the internet to the systems with `MX' or `A' records. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: comp.unix.shell, comp.sys.sun.misc, comp.sys.sun.admin, comp.protocols.tcp-ip Followup-To: comp.sys.sun.admin From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 4 Jun 92 22:11:43 GMT Subject: Unix shell TCP tools and /usr/etc/mconnect bug I occasionally write simple TCP clients as a shell script. The only tool I really need for the job is a filter that will connect the standard input and output to the streams of a TCP connection. Once upon a time I used telnet as the filter, but that had a problem: When the connection dropped, you would lose the end of the output--sometimes all the way back to the beginning. So I was happy to see mconnect(8) in the Sun distribution (did Sun write it, or is from BSD?) because it does exactly the right thing for me--almost. It has three problems, and two of them are minor. The third, however, is a fairly severe bug, and I would like suggestions for solving it. Problem 1: Mconnect does not translate NETASCII back to ASCII, so you get carriage returns (^M) in the output. I pipe the output through tr -d '\015' and that solves the problem. It would be faster, though, if mconnect did the translation. Also, I'm a little concerned that mconnect may not be inserting carriage returns on input, though I haven't run into problems with that yet. Problem 2: Mconnect prints connecting to host nic.ddn.mil (192.112.36.5), port 101 connection open at the beginning of the output. But most tcp services put out some sort of initial greeting that I have to ignore anyway, so ignoring two more lines is no problem. Still, this stuff should be on stderr. Problem 3: Mconnect SOMETIMES inserts connecting to host nic.ddn.mil (192.112.36.5), port 101 connection open at some random place in the output. It is apparently timing dependent, and I have no source to find out where it's coming from, and I really don't want to have to delete those lines when they could be valid output. For instance, the command echo ALL-MIL | /usr/etc/mconnect -p 101 nic.ddn.mil | grep -n connect gives me output like 1:connecting to host nic.ddn.mil (192.112.36.5), port 101 2:connection open 1436:connecting to host nic.ddn.mil (192.112.36.5), port 101 1437:connection open where the second set of line numbers occur somewhere between 1000 and 5000. Has anyone fixed the problem 3 bug? Is there a publicly available version of mconnect or equivalent? So far I've found "tcpcon" in Simtel20's PD6: directory, but that doesn't have the code to wait for the output to drain. Please mail me your suggestions, and I'll report any solutions that come in. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: comp.misc, comp.unix.programmer Followup-To: news.newusers.questions From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 5 Jun 92 14:28:17 GMT Subject: Re: On Holy Wars and a Plea For Peace be...@kvatro.no (Bernt Marius Johnsen) writes: >I once had a copy of an atricle on big/little endian computers called >"On Holy Wars And A Plea For Peace" by Denny Cohen, written in 1980. Available by ftp as ien/ien-137.txt on machine NIC.DDN.MIL (192.112.36.5). 36K characters. If you don't know how to ftp (or ftpmail) RTFAQ. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: dc.general From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 5 Jun 92 17:58:32 GMT Subject: Re: Fresh coffee beans willm...@beno.CSS.GOV (Raymond Willemann) writes: > Where can we find good freshly roasted coffee beans? What's so funny about care packages? I used to live off a combination of h...@eng.umd.edu (David Hsu) replies: > Roasters On The Hill (666 Penn. Ave SE, Capitol Hill) is the only local > joint I've heard of which roasts their coffee fresh.... Java House, at 17th and Que Streets NW, roasts their beans in the store. I don't know how frequently. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: sci.math From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 11 Jun 92 16:05:22 GMT Subject: Re: Square Fibonacci numbers (Summary) membrillo@vax.oxford.ac.uk writes: > Question: What are all the square Fibonacci numbers? > Answer: The square Fibonacci numbers are {0,1,144}.... > Moreover Ray Steiner proved in 1967 that the cube Fibonacci numbers > are {0,1,8} You might want to consider F[-2]=-1 and F[-6]=-8 as well. Of course, F[-12]=-144 doesn't count because it isn't a square, though we may wish to count F[-1]=F[1]=F[2]=1 three times. Or not. So are any other Fibonacci numbers the Nth power of an integer, N>1? Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: sci.math.symbolic From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 11 Jun 92 16:58:11 GMT Subject: Re: Case in symbolic math names. jaf...@zurich.ai.mit.edu (Aubrey Jaffer) writes: >`COSH' vs. `cosh' vs. `Cosh' seems an inconvenient distinction. >However `V' vs. `v' is a useful distinction and is often used for >distinguishing vectors from scalars. Do people like upper and lower >case distinguished for other than single letter variable names? Welcome to the case-distinction tar pit, where even the largest dinosaurs fear to tread. If `V' should be distinct from `v', then shouldn't `VPrime' be distinct from `vPrime'? Or should those be `V_Prime' and `v_prime'? And how about distinguishing `Gamma' from `gamma'? If you are programming in a character set that has bold and italic characters, shouldn't those other renditions of `v' be distinguished as well? Unfortunately, you quickly come to the conclusion that if you allow these exceptions, then you should distinguish case everywhere, for otherwise no one can tell which names are the same and which are different. On the other hand, we can refuse to distinguish variables by case or rendition, and use names like `CapitalV' and `LittleV' for distinguishing scalars from vectors. My own opinion is that the problem should be mootified by outlawing single-letter names entirely. They are, after all, insufficiently descriptive of their use. This opinion does not, however, prevent me from using such names in my code. I would suggest that anyone sufficiently masochistic to want to debate this topic should try the tar pits over in comp.lang.misc. You don't think symbolic mathematicians were the first to run into this problem, do you? There is an amusing parallel to the original rules for distinguishing names in the TEX typesetting language, but I digress. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: sci.chem From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 11 Jun 92 21:27:18 GMT Subject: Sodium Iodide content of Tincture of Iodine For water purification, the rec.backcountry FAQ Panel 9 says: >Also avoid tincture of iodine, which contains more sodium iodide than >pure iodine; sodium iodide has no disinfectant properties. Now tincture of iodine is supposed to be a solution of iodine in alcohol; NaI if present is an impurity. I imagine that Wilkerson's "Medicine for Mountaineering", from which this statement has been taken, is simply mistaken. Does anyone have a reference for the amount of NaI that can be present in tincture of iodine? Or has any reader actually measured it? Note that I'm not taking issue with the lack of disinfectant properties of NaI, but with the amount of it in iodine tincture. Tangentially, my vague recollection is that iodine added to a solution of NaI dissolves and becomes colorless. What is the reaction here, or am I just mistaken? This is not particularly relevant to the question of NaI in tincture of iodine, except that it would probably mean that such a mixture would be colorless. Dan Hoey@AIC.NRL.Navy.Mil --- Newsgroups: sci.math From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 17 Jun 92 15:09:37 GMT Subject: Re: Tic-Tac-Toe and 4-d magic hyper-cubes p...@nprdc.navy.mil (Larry Pugh) writes: > I believe that the following method of recording a > tic tac toe game will avoid the need to keep track of a lot of > rotations, etc. Number the grid as a 3x3 magic square, for > example: > 2 9 4 > 7 5 3 > 6 1 8 > Now the game becomes one of taking turns choosing a number > from 1 to 9. The first side to select exactly three numbers having > a total of 15 wins. All you have to do is keep track of the numbers > chosen by each side. Whenever a side has exactly three numbers totaling > 15 then they win. If all nine numbers have been drawn and no combination > of three numbers totals 15 then the game is drawn. Well, Jeff Eppler wasn't asking how to *avoid* keeping track of rotations and reflections, he was asking how best to *use* them as a tool to cut down on the size of the search space. You don't need to keep track of rotations and reflections even with a more traditional form of board recording, it just means you have to analyze the eight positions X O . . O X . . X . . . . . . . . . . . . X . . . . . . . . . O . . O . . . . . . O . . O . . . . . . . . . . . . X . O X X O . X . . . . . separately, instead of noticing they are equivalent and only examining them once. Similarly, the magic square approach obscures the fact that after the first two guesses there are only ten essentially different positions, not 72. That said, the idea of transforming tic-tac-toe into a magic square puzzle is neat. You can also transform it into a word game, picking letters until you get a set that will spell one of eight three-letter words. There's an article on this in Martin Gardner's collection Mathematical_Carnival. marwk@levels.unisa.edu.au writes: > Do you, or anyone else, know of a 4-dimensional 4*4*4*4 magic > hypercube so that all 512 possible winning combinations would be the > simple sum of 4 numbers to form a fixed total? Wrong number. In the 4^4 tic-tac-toe board, there are 520 winning combinations: 256 rows where one coordinate varies, 192 rows where two coordinates vary, 64 rows where three coordinates vary, and 8 rows where all four coordinates vary. You probably failed to count the last set, which is a little harder to visualize since it doesn't lie in any three-dimensional slice of the puzzle. But all of these sets are usually considered winning combinations in four-dimensional tic-tac-toe. Strangely enough, I have been told that most of the magic cube and magic hypercube literature only accepts the first two sets as the rows that must sum to a fixed number, no matter how high the dimension gets. I think that's playing with the net down, but that's the literature. I'm pretty sure that the usual way of composing magic cubes, using the numbers from 1 to N^D, will not work for large tic-tac-toe boards, because there are many more subsets of N elements summing to N(N^D+1)/2 than the number of winning combinations, ((N+2)^D-N^D)/2. I haven't done the combinatorics on it, but I suspect that the 3^2 board is the only nontrivial one where it will work. I wouldn't be surprised, though, if it can be done by labeling the points with a sparser set of numbers. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: rec.puzzles From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 22 Jun 92 21:57:11 GMT Subject: Re: CHOMP dwr2...@zeus.tamu.edu (RING, DAVID WAYNE) writes: > Here is my list of winning positions: > {(1,0,0),(0,1,0),(0,0,1)} > {(1,0,0),(0,1,1),(0,0,N),(0,N,0)} > {(1,0,0),(0,1,1)} > {(1,0,0),(0,0,N),(0,1,N-1)} ^^^^^^^^^^^^^^^^^^^^^^^^^^^ I think you need to include (0,2,0). > {(1,0,0),(0,2,0)} > {(1,0,0),(0,3,0),(0,1,2),(0,0,4)} > {(2,0,0),(1,1,0),(1,0,1),(0,3,0),(0,2,1),(0,1,2),(0,0,3)} > {(2,0,0),(1,1,0),(1,0,1),(0,3,0),(0,2,2),(0,0,3)} .. > BTW could someone who read the book tell us the state of the art, maybe > all this is a waste of time. Well, if you mean Winning_Ways, I doubt that it's the state of the art. They only describe two-dimensional bounded chomp, in which at least (1,0,0), (0,N,0), and (0,0,M) have been played, for some M and N. They do, however, have a lot of information about such positions. I've typed nearly all of it below, with some comments and questions. Besides the show the first, second, and fourth (amended) position on your list, they have {(1,0,0),(0,3,0),(0,2,2),(0,1,2+N),(0,0,4+N)} for N>=0, which includes your sixth position as a special case. They also have the following table, containing values of A for which {(1,0,0),(0,3,0),(0,2,C),(0,1,B+C),(0,0,A+B+C)} is a winning position: B\C 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 0 1 2 2 3 4 5 5 6 7 7 8 9 9 11 11 12 12 13 14 15 15 16 17 17 18 19 19 1 1 0 2 3 4 3 5 6 5 7 8 7 10 9 11 10 12 13 14 13 15 16 15 17 18 17 20 2 . . . 0 4 4 5 3 6 3 8 9 8 7 7 11 8 10 11 14 15 13 16 17 18 19 18 3 . . . . 0 4 0 5 6 6 8 3 9 9 10 11 12 12 8 14 10 15 16 12 18 13 19 4 . . . . . . . 5 0 6 0 8 3 9 10 11 10 12 13 8 14 8 10 16 10 18 13 5 . . . . . . . . . . . 8 0 9 3 3 11 12 11 13 14 15 15 8 17 8 18 6 . . . . . . . . . . . 8 . 0 9 10 11 3 12 13 14 13 15 16 17 17 18 7 . . . . . . . . . . . 3 . . 9 0 0 11 12 3 14 14 15 16 10 13 8 8 . . . . . . . . . . . 7 . . . . . 11 0 12 3 14 3 13 16 16 17 9 . . . . . . . . . . . 7 . . . . . . . 12 0 14 14 15 3 16 3 10 . . . . . . . . . . . . . . . . . . . . . 0 14 0 15 16 16 11 . . . . . . . . . . . . . . . . . . . . . . . . 15 0 16 I don't know what the dotted entries mean; they are simply left blank in the book. It seems to me that column 2 should be filled with 2's, by the general position I mentioned above. Also, column zero should be filled with 1's by your (amended) general position four. But I think column 1 should be blank for B>1 because there is no solution: (0,1,1) is an answer for B=2,C=0, and (0,0,3) is an answer for any other case. Perhaps I have misunderstood or overlooked something. They also note that {(1,0,0),(0,A,0),(0,0,B)} is lost unless A=B=1. They have the following table of responses, where CxD means to move (0,A-C,B-D). They note that the reply is unique when A or B is at most 3, but that Ken Thompson found two winning moves, 4x5 and 5x2, for A=8,B=10 (*). A\B 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1 lost 1x1 1x2 1x3 1x4 1x5 1x6 1x7 1x8 1x9 1x10 1x11 1x12 1x13 1x14 1x15 2 1x1 1x1 1x1 1x1 1x1 1x1 1x1 1x1 1x1 1x1 1x1 1x1 1x1 1x1 1x1 1x1 3 2x1 1x1 2x2 2x2 1x2 2x3 1x3 2x4 1x3 2x5 2x5 1x4 2x6 1x4 2x7 2x7 4 3x1 1x1 2x2 3x3 2x3 3x4 2x4 3x5 5 4x1 1x1 2x1 3x2 4x4 3x3 4x5 6 5x1 1x1 3x2 4x3 3x3 5x5 7 6x1 1x1 3x1 4x2 5x4 6x6 8 7x1 1x1 4x2 5x3 7x7 (*) Finally, they note that {(1,0,0),(0,X,0),(0,2,1),(0,1,B),(0,0,A)} is a winning position if X=floor((2A+B)/2) and A+B is even, or if X=min(ceiling((2A-B)/2),ceiling(3(A-B)/2)) and A+B is odd. They used two techniques to get these results, a tabular technique and a clique technique. I think the tabular technique is essentially the dynamic programming approach you mentioned. My understanding of the clique technique is that we prove a position to be a winner by partitioning the set of moves into subsets C1,C2,... (called cliques) such that 1. There is a winning reply in Ci to each move in Ci, and 2. After a move and its reply in Ci, there are no moves in Cj for j>i. I think they may have relaxed rule 2 in some cases. But basically they use this to cut down on the size of the game tree for games in which the order of preceding moves is irrelevant to the remainder of the game. I think the term ``clique'' is misleading here, since for the cliques of more than two elements it may not be the case that every element is a winning reply to every other. But I think they mean the clique technique to be a generalization of the more common ``pairing technique'' in which each move and its response are also vice versa. For {(1,0,0),(0,1,1)} and {(1,0,0),(0,1,1),(0,0,N),(0,N,0)} the cliques are {(0,0,M),(0,M,0)}. For {(1,0,0),(0,2,0)} and {(1,0,0),(0,2,0),(0,1,N),(0,0,N+1)} the cliques are {(0,1,M),(0,0,M+1)}. For {(1,0,0),(0,3,0),(0,2,2),(0,1,2+N),(0,0,4+N)} the cliques are {(0,1,0),(0,0,1)}, {(0,2,1),(0,0,2)}, {(0,1,M),(0,0,M+2)} for M To: Cube Lovers Subject: Re: Ultimate cube MONET01@mizzou1.missouri.edu writes of a cube that ``looks like someone took a knife to a normal solved cube and cut a diagonal 'x' through each face and folded the flaps back down the sides. This leads to a cube where opposing centers have an 'x' that has four colors in a mirror image. (It is hard to describe, sorry.)'' I would appreciate a few more details. I think the color scheme of each face you describe is something like +-----+-----+-----+ |.1111|11111|1111.| |44.11|11111|11.22| |4444.|11111|.2222| +-----+-----+-----+ |44444|.111.|22222| |44444|44.22|22222| |44444|.333.|22222| +-----+-----+-----+ |4444.|33333|.2222| |44.33|33333|33.22| |.3333|33333|3333.| +-----+-----+-----+ where 1,2,3, and 4 are distinct colors, but there are still several ways to make the colors on different faces match up. Look at a corner, where the colors are +-------+ /a.bbbbb/c\ /aaa.bbb/ccc\ /aaaaa.b/ccccc\ +-------+.......+ \fffff.e\ddddd/ \fff.eee\ddd/ \f.eeeee\d/ +-------+ That is, one corner is colored a/b, another c/d, and the third e/f, where I expect some of a,b,c,d,e,f will be the same color. One possibility was pictured in Hofstatder's Scientific American article of February, 1981. It had b=c,d=e,f=a and used twelve colors. Jim Saxe and I were impressed by its wasteful use of color and its failure to exhibit edge orientation. From your remarks about turning it over, I suspect this isn't what you mean. You may be talking about the cube in which a=d,b=e,c=f which uses six colors. I would say it is as if you cut an 'x' on a cube and exchanged each triangle with the other triangle on the same edge of the cube. That is a reasonably good coloring. It isn't really necessary to solve it twice, though. To find out whether a given corner goes on the top or bottom, look at the two colors that the corner shares with the top face center. Either the corner will have the two colors in the same order as the top, or they will be reversed, and that determines whether that corner goes on the top or bottom. That tells you where the third color on that corner goes, and the last color is determined by elimination. There is an even more interesting coloring that uses only four colors. In this coloring a=c=e and the other three colors are distinct. Jim Saxe and I came up with this coloring in our discussions of Hofstatder's article. It isn't quite symmetric enough, since its reflection is a coloring in which b=d=f, a slightly different pattern. Our discussions then led to the Tartan coloring we talked about in our article of 16 February 1981. The only cube in the archives called the Ultimate Cube is the one that has ``over 43 quintillion solutions.'' It has all six sides colored the same. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: sci.math From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 27 Jun 92 18:54:31 GMT Subject: Re: Fermat's Last Theorem endic...@carina.unm.edu (Mark Endicott) asks: > A few years ago some mathematician announced a proof of Fermat's > Last Theor[e]m.... Does anyone know what happened, and where I can > find the proof? You are probably thinking of the work of Yoichi Miyaoka (Tokyo Metropolitan University, then at the Max Planck Institute for Mathematics, Bonn). He thought he had the outline of a proof, and it got into the press in March, 1988. But flaws were found. Some of the gaps in the outline were known to be false in similar cases, so his plan of proof could not work. By the end of March it was clear there was no proof. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: bit.listserv.asm370 From: Dan Hoey Date: Tue, 30 Jun 1992 12:13:50 -0400 Subject: Re: Strange use of compare-and-swap you write: >If the routine which is zeroing the counter cares about the exact value >that the counter had before it gets zeroed, then you must use the CS >instruction (although your loop is two instructions too long, it >*should* be coded: > XR 0,0 > L 1,COUNTER > LABEL CS 1,0,COUNTER > BNZ LABEL >since R0 doesn't need to be re-zeroed and, if the CS instruction fails, >it will load R1 with the *new* value of COUNTER, so you are ready to do >the CS again). Presumably, after this loop you will then do something >with the "old" value that is now in R1. Surely you mean to put LABEL on the L instruction, not the CS. Or is my unfamiliarity with this particular assembly language playing me tricks? Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: sci.math.symbolic, sci.math, sci.math.num-analysis, misc.forsale Followup-To: misc.forsale From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 7 Jul 92 21:06:32 GMT Subject: Re: Are there any public domain symb.math pkgs? In sci.math.symbolic, lace...@cs.UAlberta.CA (Winslowe Lacesso) asked: >Please send any info you might have on public domain symbolic math >packages, to d...@odin.uniras.dk (Douglas Nadworny), or if that bounces, >to me (lace...@cs.ualberta.ca), & I will forward to him. In several newsgroups, hu...@deakin.OZ.AU (Weiguang Huang) replied: > I suggest you consider SymbMath. [advertisement deleted] I suggest you avoid SymbMath for the following reasons: 1. It is not what you asked for. You asked for public domain software, and SymbMath requires a license. Even if you just wanted a free package, Dr. Huang charges money for SymbMath. 2. It is apparently not very good. Even when Dr. Huang found a review of his product in Australian PC Week, the best thing they could say about it was that it uses less memory than Mathematica. 3. It promotes network abuse. Dr. Huang repeatedly posts his advertisements for this commercial package to a large number of technical newsgroups, in which advertising is not welcome. If you buy his software, he will be encouraged to post more advertisements. Worse, you encourage other parasitic marketers to advertise in the technical groups. For these reasons, I urge you to boycott Dr. Huang's SymbMath software. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: sci.math From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 7 Jul 92 21:29:31 GMT Subject: Re: Unfoldings of a hypercube orou...@sophia.smith.edu (Joseph O'Rourke) writes: >Does anyone know how many distinct unfoldings there are of a >hypercube (a 4-dim cube)?.... oconn...@unix1.tcd.ie (Frank D. O'Connor) suggests we add up the number of neighbors of each face. > For the cruciform development of the hypercube shown in > Rucker, the numbers of adjoining cubes for each cube sum to 14. > It may, or may not be, that all possible developments must have > this sum of 14. Yes, but that is far too weak a condition to be useful. In any connected, acyclic arrangement of N adjacent objects, the sum of the number of neighbors will be 2N-2. This is a consequence of the fact that any tree on N vertices has N-1 edges. But there are many such arrangements, and relatively few of them can be the unfolding of the D-dimensional cube. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: sci.math, rec.puzzles From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 14 Jul 92 21:21:23 GMT Subject: Re: Chomp wo...@bmerh707.bnr.ca (Ian Woollard) writes: > I contend that if there are no patterns of wins in cubes of side n > as n goes to infinity, then there can be no answer. In case John Rickard did not sufficiently lay this one to rest, I would remark that it is not correct even in the two-dimensional case. There is no known pattern of wins on square boards, but there is a known strategy that wins on the infinite two-dimensional board. I think it may indeed not be possible to prove who has the win in infinite chomp, but I don't know of a criterion for such a result other than that no such proof exist. I wonder if it's conceivable that chomp could be proved to be undecidable. (I should probably not wonder such things aloud, as I have always before been deluged with incorrect proofs of impossibility.) jrick...@eoe.co.uk (John Rickard) writes: > Incidentally, it's easy to prove that on any cuboidal board bigger > than 1x1x1 the first player can win; I don't know whether anyone's > pointed this out yet. I pointed this out in the two-dimensional case based on the remark in _Winning Ways_ that it's a straightforward theft of strategy. I wondered how until just today, when it struck me. On a cuboidal board there is a single move (denoted 111 in the table below) that prevents no other move but is prevented by each other move. If 111 wins, the first player should play it. Otherwise, there is a winning response to 111, and the first player should play the response. The key observation is that the response alone leaves the same position as 111 followed by the response. (If you know of a different proof of this result, please drop me a line.) dwr2...@zeus.tamu.edu (Dave Ring) mentioned that he and I have recently hacked on 3 dimensional Chomp on small cuboids. Results up to the 5x5x5 case are given below. ABC:DEF,GHI means that in response to {(A,0,0),(0,B,0),(0,0,C)} you should play (A-D,B-E,C-F) or (A-G,B-H,C-I). 222:111 322:111 332:111 422:111 432:322 442:221 522:111 532:331,521 542:111 552:311,221 333:222 433:111 443:223,311 533:222,511 543:332 553:431 444:211 544:222 554:334 555:421 Unfortunately, 666 seems to be out of the question without some major improvements in the algorithm. We should probably infer something infernal from that. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: rec.puzzles, sci.math From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 17 Jul 92 17:50:31 GMT Subject: Unavoidable sets of congruences (was The Erdos kitty) g...@manifold.berkeley.edu (Greg Kuperberg) posted the problem: > A set of congruences n = a_1 mod b_1, n = a_2 mod b_2,... is > unavoidable if each n satisfies at least one of them. Is there an N > such that every unavoidable set of congruences either has two equal > moduli b_i and b_j or some modulus b_i less than N? dwr2...@zeus.tamu.edu (Dave Ring) says it is easy to prove there can be no such N if n is restricted to the natural numbers. I suspect his counterexamples are infinite sets of congruences, though. As cour...@corvette.ens.fr (Francois Courtes) noted, if the set of congruences may be infinite the theorem is obviously false. Take the congruences n = 0 mod N, n = -1 mod N+1, n = 1 mod N+2, n = -2 mod N+3, n = 2 mod n+4, ..., n = -k mod N+2k-1, n = k mod N+2k, .... All moduli of this unavoidable set are distinct and at least N. brns...@nyu.edu (Dan Bernstein) suggests we transform the set of congruences to n = -a_1 mod b_1, n = a_1 mod b_1, n = -a_2 mod b_2, n = a_2 mod b_2, ..., but that is not a faithful transformation, because it introduces equal moduli. Dan also considers the term ``whole number'' nicer than ``nonnegative integer,'' but the former term seems to me to be ambiguous. I could not tell without a gloss whether ``integer,'' ``positive integer,'' or ``nonnegative integer'' is meant. Dan also recalls that ``Erdos was talking about finite sets of congruences anyway.'' Due to the counterexample, I think this must be so, and Greg ought to make this clear in the problem statement. Therefore it doesn't matter whether or not we restrict n to the integers. In fact, we can restrict the problem to 0 <= n < lcm(b_1,b_2,...) without loss of generality. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: talk.bizarre From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 22 Jul 92 21:21:23 GMT Subject: Re: I don't know... I don't know, I've never anythed. I've never batwed. I've never bedspred. I've never Beijed (nor Peked, in earlier years). I've never bed (cherry, that is). I've never bluestocked. I've never Boeed. I've never Chungked. I've never cled (peach, I suppose). I've never cunned (low). I've never Cushed (a cardinal). I've never darled. I've never ded. I've never Dowled. I've never Downed ten. I've never duckled. I've never earred. I've never everythed. I've never Ewed. I've never Flemed. I've never fled. I've never foundled. I've never gosled. I've never gunsled. I've never Harded. I've never hireled. I've never inkled, not the slightest. I've never Irved. I've never Ised. I've never Kettered. I've never ked. I've never lacewed. I've never Lansed in Michigan. I've never lemmed. I've never lightned, though it shocks you I know. I've never mudsled. I've never Nanked. I've never nothed. I've never Pershed. I've never Pickered. I've never ped. I've never playthed. I've never Poynted. I've never pudded. I've never red. I've never sanderled. I've never sapled. I've never schelled. I've never seedled. I've never shoestred. I've never sibled. I've never sed. I've never sled. I've never somethed. I've never spalded. I've never sparled. I've never Spaulded. I've never spred. I've never starled. I've never sterled. I've never sted. I've never Stirled. I've never stred. I've never swed. I've never thed. I've never Tured. I've never underled. I've never upswed. I've never Viked. I've never Wared. I've never wed. I've never Wyomed. I've never zed. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: rec.puzzles From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 23 Jul 92 11:21:32 GMT Subject: Re: Plane Division s...@brems.ii.uib.no ( Per Ivar Roervik) writes: > In a closed and bounded area of any 2-D shape, 1 million random > points are chosen. > Is it always possible to bisect the area AND the points into two > equal parts with a straight line? Several respondents have offered counterexamples, but they all involve lots of collinear points and the inability to avoid some of them. Suppose we allow a line through some points to `divide' those points in whatever way makes the overall division most even. So if a line goes through 500,000 points, it will perforce divide the set of one million in half. I am pretty sure the answer in this setting is yes. It's essentially a kind of ham sandwich theorem. The ham sandwich theorem says that no matter how sloppily you make a ham sandwich, it's always possible with one knife cut to bisect both the ham and the bread. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: rec.puzzles, sci.math Followup-To: rec.puzzles From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 25 Jul 92 22:13:33 GMT Subject: Digital Invariants (was Number Theory) uunet!eliot!andyc (Andy Panda Collins) writes: > I don't know much about this news-group, but I thought > that I might post this list of number-theoretic numbers. > Let N be an n-digit number which is separated into it's > decimal digits, raise each digit to the nth power and sum > them. Let N be a unique number if the sum is equal to N. Well, this topic is more the province of recreational math than of number theory, so I've redirected it to rec.puzzles such topics are more customarily treated. According to David Wells's book _The_Penguin_Dictionary_of_Curious_ _and_Interesting_Numbers_ these numbers are called digital invariants. Wells notes that When G. H. Hardy wished, in his book _A_Mathematician's_Apology_, to give examples of mathematical theorems that were not `serious', he chose two examples, `almost at random', from Rouse Ball's _Mathematical_Recreations_. The first was the fact that 8712 and 9801 are the only 4-digit numbers that are multiples of their reversals. The second was the fact that, apart from 1, there are just 4 numbers that are the sums of the cubes of their digits. I found all the numbers that are multiples of their reversals last year (and coined the term `palintiples' to refer to them) so I suppose it is not so surprising that I should be interested in this problem as well. Andy lists all the digital invariants up to 14 digits, and I wrote a program that confirms his list. The next few are: 15 digits: none 16 digits: 4338281769391371 4338281769391370 17 digits: 35875699062250035 35641594208964132 21897142587612075 18 digits: none 19 digits: 4929273885928088826 4498128791164624869 3289582984443187032 1517841543307505039 20 digits: 63105425988599693916 21 digits: 449177399146038697307 128468643043731391252 22 digits: none 23 digits: 35452590104031691935943 28361281321319229463398 27907865009977052567814 27879694893054074471405 21887696841122916288858 24 digits: 239313664430041569350093 188451485447897896036875 174088005938065293023722 25 digits: 4422095118095899619457938 3706907995955475988644381 3706907995955475988644380 1553242162893771850669378 1550475334214501539088894. I have also verified that there are no digital invariants of 46 or more digits. David Wells lists one more digital invariant, though, of 39 digits: 115132219018763992565095597973971522401 and he says it is the largest one known. However, I am not sure but what this may have been proven to be the largest one that can exist by whoever discovered it. I do wish Wells were a little more conscientious with his attributions. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: rec.puzzles From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 3 Aug 92 21:21:23 GMT Subject: Re: Gummy Drop-bears (spoilers and discussion) In a newsgroup clogged with vacuous inanities, endless quibbles over carelessly posed problems, futile FAQs, definitions of decimals, and now even the noisome overflow from sci.physics, it is most refreshing to see cl...@remus.rutgers.edu (Chris Long) favor us with a new, interesting puzzle: > Real gummy drop-bears mass 10 grams, while imitation gummy > drop-bears mass 9 grams. Spike has 7 cartons of gummy drop-bears, 4 > of which contain real gummy drop-bears, the others imitation. Using > a scale only once and the minimum number of drop-bears, how can > Spike determine which cartons contain real gummy drop-bears? k...@cs.cornell.edu (David Karr), d...@hpnmdla.sr.hp.com (Dan Merget), and a...@troi.cc.rochester.edu (Andrew Markiel) all provided the 51-bear solution of taking 0, 1, 2, 4, 7, 13, and 24 bears from the respective boxes. Certainly that selection serves to distinguish the possible sets of imitations, but I would like a proof that this set is the bear minimum. I already have a program that says so, but I have a fondness for succinct proofs. And the methods of David, Dan, and Andrew are not apparently rigorous in determining the minimal solution. Andrew got the solution by starting with 0, 1, and 2 and making the other numbers be the sum of the previous three. But if Spike had ten cartons among which to determine the three cartons of imitations, Andrew would tell him to take 0, 1, 2, 4, 7, 13, 24, 44, 81, and 149 bears from the respective cartons. Spike could do better by taking only 139 from the last carton, and still determine the bogus bears in a single weighing. David and Dan appear to proceed by taking the minimum possible from each box in turn, such that they find a solution. But this is a greedy algorithm, in which by taking fewer bears from one carton they might conceivably force themselves to take more bears from a later carton. For instance, if Spike had EIGHT cartons, only TWO of which were fake, David and Dan would have him choose 0, 1, 2, 4, 7, 12, 20, and 29 bears from the respective cartons. But that requires 75 bears, while a 72-bear solution exists: 0, 1, 2, 4, 8, 14, 19, and 24 bears. Searching for a case in which the greedy algorithm does not provide an optimal solution for identifying three bogus cartons turned out to be surprisingly difficult, though. My program tells me that greed is a perfectly good strategy up to ten boxes. But for finding three bad cartons in a consignment of eleven, the greedies would have us take 0, 1, 2, 4, 7, 13, 24, 44, 81, 139, and 234 bears, for a total of 549. We can, however, save eleven bears by taking 0, 3, 5, 6, 7, 14, 25, 44, 79, 133, and 222 bears. (The program for this takes a long time. It has not yet concluded that this is the optimum, though I suspect it will soon. It has already elminated all cases in which the second number is less than 13.) I imagine this problem must be addressed in the literature somewhere, and I would appreciate a word from anyone who recognizes it. Especially if the literature has some approaches to succinctly proving optimality. I expect that with a little work we can shew the optimality of the solution for the original seven-carton problem, in a way that could be appreciated by a human. But barring some truly amazing insight, I suspect the proof for the eleven-carton problem is reading matter for our electronic brethren only. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Date: Mon, 03 Aug 92 11:10:29 -0400 (EDT) From: Dan Hoey To: Cube Lovers Subject: Re: cube theory Dear Mark, I sent you email on 8 June. Did you receive it? Are you interested in acquiring a Tartan cube? Did you ever get Minh Thai's book on Rubik's Revenge? With respect to the 3x3x3 squares group, How do you keep track of all the patterns without repeating yourself? there are several ways. The most general is to use the Sims table (aka the FHL table) for the subgroup, which gives a mixed-base enumeration of the positions. See my message of 1 February 1981. A local maxima is a state where any possible move will bring you closer to a solution. That's ``local maximum''. ``Maxima'' is the plural of ``maximum''. Note that all possible patterns at maximum depth are local maxima, .... We call such positions ``global maxima'' because they are at the overall maximum depth. The statement is then that every global maximum is a local maximum. To date, no work has been done to determine the depth of the dodecahedron (megaminx).... Well, I've done some looking at it. Since my initial remarks on 23 September 1982, I've figured out a way to generate a recurrence for it, but it seems I haven't put it down anywhere. Are you interested? (Do I have to tell anyone to answer that question only to Hoey@AIC.NRL.Navy.Mil, not the list?) What pattern is an example of local maxima? e.g. 3x3x3 at depth 3 -> 12-flip, 12-flip 8-twist Jim Saxe and I listed the 25 symmetric local maxima in our message on Symmetry and Local Maxima, dated 14 December 1980. We verified Jim's conjecture that the four-spot is a local maximum, but not on the grounds of symmetry, and reported that on 22 March 1981. Do you have access to the cube-lovers archives? Moves Deep arrangements (q+h) arrangements (q only) * 0 1 1 1 18 12 2 243 114 3 3,240 1,068 4 > 48,600 10,011 This is in the archives, too 5 93,840 (22 March 1981) 6 878,880 (14 August 1981) 7 8,221,632 (7 December 1981) David C. Plummer and I had hoped to use his program (which counted the 7 QT positions) to extend this to 8 QT, but we got busy. I still have hopes.... At 2 moves deep it is redundant to turn the same side again.... However, with opposite turns order is not significant, e.g. T,D = D,T.... This approach appeared on 9 January 1981. It showed how to follow the argument to 25 QT, and to get what are still the best known lower bounds for the ordinary cube and for the supergroup. Also what is an example of a local maxima close to the surface, e.g. 4 moves. I believe Jim Saxe and Dan Hoey have done some work in this regard. It's known there are no local maxima at 7 QT or less. The shortest known local maxima are Pons Asinorum and the four-spot, both at 12 QT. I know of no results between 8 and 11 QT. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: rec.puzzles From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 4 Aug 92 12:39:34 GMT Subject: sod.! (was a series problem and answer) In response to the series question >> >3 6 9 27 ? dwr2...@zeus.tamu.edu (Dave Ring) gave: >> 3^3^3, whatever that means. explaining > the first term '3' is a little ambiguous, but is reasonable. I have to take exception to that: One of the rules of the sequence of arithmetic operations is that op[k](n,n)=op[k+1](n,2) so whatever op[0] is that comes before op[1]="+", it must satisfy op[0](3,3)=3+2=5, not 3. Otherwise, I have to grant that Dave made a valiant try at providing interesting answers to a couple of pretty mediocre puzzles (and if ``there are no bad questions'' then the ``good'' questions that are bad puzzles belong in rec.questions, not here. (No, it doesn't exist. BFD, CFD.)) Series puzzles are generally pretty lousy, partly because they are so ambiguous (and for all the people who have asked for the ``simple'' rule I have yet to see a proof of optimum simplicity, or even a decent attempt to frame a useful measure) and partly because they are usually followed by a couple of dozen reposts of the audioactive sequence (series.07 in the FAQ). But this problem, before it was melted down into a series puzzle, was actually about a fairly interesting function, sod.!, where sod.!(n) is the sum of the digits of n!. So tell me, for how many pairs n > m+1 is sod.!(n) = sod.!(m), or if infinite, how big can n-m get, or if infinite, how big can n/m get? Are there any interesting results beyond the fact that for n>5, 9|sod.!(n)? Is there even a proof that sod.!(n)>9 whenever n>8? I wish this were a better puzzle, but it's probably just some questions. I hope at least they are not quite so trivial, ambiguous, and trite as the other ones I saw today. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: rec.puzzles From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 4 Aug 92 20:45:11 GMT Subject: Prime of concatenated primes (spoiler) che...@gsusgi1.gsu.edu (Parthasarathy Nambi) writes: > 23, 235, 2357, 235711, etc Do you see the pattern? > In the above sequence 23 and 2357 are primes. Actually > 2357 is a fascinating prime (more about it later). > I have continued this series of numbers upto the prime 103, and haven't > found any other prime - if one can *believe* Mathematica's PrimeQ test. according to Mathematica, 2,357,111,317,192,329,313,741,434,753,596,167,717,379,838,997,101,- 103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,- 191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,- 277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,- 379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,- 467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,- 587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,- 677,683,691,701,709,719 is the next prime in the sequence. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: rec.puzzles From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 7 Aug 92 21:06:42 GMT Subject: Re: Gummy Snipes (spoiler) cl...@remus.rutgers.edu (Chris Long): : Spike has six cartons of gummy snipes. Some or all of the cartons : may contain imitation gummy snipes, which weigh more or less than : real gummy snipes, this difference being exactly the same for all : such snipes. Given that a real gummy snipe has a mass of 10 grams : and using a scale only twice, what is the minimum number of gummy : snipes Spike would need to use in order to determine which cartons : contain contain real gummy snipes and which cartons contain : imitations? Nice. My program tells me he needs 28 snipes. Weigh 1,2,2,5,5,0 and 0,2,1,1,8,10. I haven't yet verified this by hand. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: news.admin.policy, news.groups Followup-To: news.admin.policy From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 14 Aug 92 18:03:24 GMT Subject: Re: STRAW POLL: changing a moderator j...@athena.mit.edu (Jonathan I. Kamens) writes: >Those of you who haven't been following the discussion in news.groups >should know that dae...@desire.wright.edu is very strongly on one >side.... I am on the other side of the debate, and I therefore chose >to add these two questions to my response to his poll: As long as we're adding questions to the poll, well, I had a hard time responding to the poll at all, since most of the questions seemed to be aimed at finding out whether I had stopped beating my wife, and why not. So here are a couple more questions I found it useful to answer on my ballot. [vote] Kottman chose an obviously biased set of questions to ask. [vote] Bias in the questions renders the results of this poll meaningless. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: news.admin, news.admin.policy Followup-To: news.admin.policy From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 17 Aug 92 14:16:15 GMT Subject: Re: STRAW POLL: changing a moderator de...@desire.wright.edu writes: > hoey@zogwarg.etl.army.mil Dan Hoey) writes: > (news.admin.policy was the followup, be we don't get it yet) >> [vote] Kottman chose an obviously biased set of questions to ask. > No. Maybe I should remind you that your posted vote can't be counted? Dan --- Newsgroups: sci.physics.fusion From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 17 Aug 92 17:59:43 GMT Subject: Fleischmann interview in JIR The latest issue of the Journal of Irreproducible Results has an interview in which Martin Fleischmann comments on the recent rumors. I could try to excerpt it if there is interest, though it's somewhat difficult to find a happy medium between giving enough detail to give you the idea of it and copying the entire article. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: sci.physics.fusion From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 18 Aug 92 17:05:23 GMT Subject: Re: Fleischmann interview in JIR [ I hope you all don't get this message twice. ] hoey@zogwarg.etl.army.mil (I) wrote: >The latest issue of the Journal of Irreproducible Results has an >interview in which Martin Fleischmann comments on the recent rumors. >I could try to excerpt it if there is interest, though it's somewhat >difficult to find a happy medium between giving enough detail to give >you the idea of it and copying the entire article. I did include ``may be harmful if swallowed'' in the Keywords line, but the Fusion Digest dropped it, so one person felt it necessary to warn me I should take JIR with a grain of salt. People have sent me email asking if I could fax the interview to them. When the long distance phone calls started, it was clear I had better start spinning this one down, so here's the scoop on the interview. The article, by Marc Abrahams, gives a short history of the cold fusion discovery and controversy, and shows a photo of Martin Fleischmann holding a cold fusion cell. It continues: During the past two years, sensational rumors have swirled abouit Fleischmann and Pons. Now, in an exclusive interview with the _Journal_of_Irreproducible_Results_, Martin Fleischmann reveals the truth about the recent rumors. The rest of the article is the interview proper. I would dearly love to include it here, but I would feel terribly guilty at reprinting what was supposed to be an exclusive interview. But I think I can fairly tell you that the only question asked was, ``Are the rumors true about you and Madonna?'' And the answer was one word long. It seems those rumors are not true. Maybe now you see why it was so difficult to find a compromise between excerpting and quoting in whole. If you still want the JIR, here's the information from the title page. The publisher is Blackwell Scientific Publications, Inc., 238 Main Street, Cambridge, Massachusetts 02142. Individual subscriptions are US $15 in the US, $20 in Canada, and $35 overseas. Phone subscriptions are 1-800-759-6102. The article is in JIR volume 37, number 4 (August 1992) on page 8. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: news.groups, rec.motorcycles, rec.motorcycles.racing, rec.motorcycles.dirt Followup-To: news.groups From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 18 Aug 92 23:46:00 GMT Subject: Re: rec.motorcycles.harley vote acknowledgment >j...@i88.isc.com (Jonathan E. Quist) writes: >>Now wait just a minute. Haven't _any_ of you ever experienced the >>variable reliability of e-mail? Does all your mail go through in >>an hour? A day? A week? If you sent some mail in, two days later >>saw a vote summary, and your name wasn't in it, would you resend >>the mail to get your vote counted, or just say, "oh, well, it'll >>count anyhow".....? st...@bucolix.ece.ncsu.edu (Steve Garnier) writes: >I briefly considered the possibility you put forth, and dismissed it. >I have never had any email delay of more than one day between university >sites and major orgs such as NASA. Ah, a newbie. You should shut up until you have enough experience to know what you're talking about. It is a good idea to look over the list and locate the suspected duplicates. To suspect, absent further evidence, that the duplicates are attempts at ballot box stuffing is ridiculous. It just goes to show that some ignorami like to be obnoxious about it. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Date: Thu, 20 Aug 92 13:51:25 -0400 (EDT) From: Dan Hoey To: Cube Lovers Subject: Re: subgroups On 14 Jan 1992, Allan C. Wechsler posted Regarding the meta-approach of descending through a series of subgroups, how much leverage does properly selecting the chain give you? It seems like the jump from to is pretty large. There are probably other paths through the subgroup lattice. Does anyone have a table of subgroups? As far as selecting the chain goes, I have been meaning to look into that a bit. Of course, since Bill posted, the results of Hans Kloosterman, Michael Reid, and Dik Winter have shown that you indeed get a lot of leverage. I would like to get some idea of the possible group towers, for a more general approach to selecting which towers give you leverage. But what I haven't been able to figure out is how to figure out which coset of G1 wrt G2 you're in. I've been able to figure it out for specific groups, but if we wanted to do this for a lot of chains, we would need to do coset identification given G1 and G2 as a table of strong generators. We could in fact ensure that the strong generators of G1 form a subset of those of G2. Is that a hard thing to do? More to the point, I've heard that the FHL algorithm should more properly be called Sims's algorithm and that Furst, Hopcroft, and Luks mostly analyzed the performance. I haven't read anything by Sims on it, though. Is there a good reference that treats this sort of algorithm in a more general setting? I have toyed with implementing the Jerrum improvements to FHL, but it is a mighty complicated beast. Also, a talk announced in the archives mentioned 1987 work by Akos Seress that was supposed to be an improvement, but I don't know whether it got published. Anyway, if not, do you know if there is a good general way of finding out which coset a given position is in. On 29 Jan 1992, wft@math.canterbury.ac.nz (Bill Taylor) posted There hasn't been any response to this, seemingly, which is a pity. For some reason, I never saw Bill's message. I just noticed it when comparing my files against the archives. [ Archives seekers note: the archives have moved to FTP.LCS.MIT.EDU (18.26.0.36), still in directory /pub/cube-lovers. ] In any event, I would like to know of any other well-known subgroups. There are the slice group; double-slice group; U group; square group; anti-slice group. How many others are there not mentioned here, that people know of ? There were some tables in Singmaster with more examples, and there are the stuck-faces groups that I wrote about on 21 July 1981. I seem to recall there was some non-obvious equivalence between two groups, perhaps the slice group and the antislice group. But a general list of popular subgroups would be interesting. Of course a list of *all* the subgroups would have, um, over three beelion of them. I suspect it has more than 4.3x10^19. Does anyone know a good way of counting how many subgroups there are? Or even a way of estimating the number? By comparison, the symmetries of the cube form a 48-element group with 98 subgroups. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: rec.humor.d From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 15 Sep 92 15:58:57 GMT Subject: Re: Hurricane Andrew In rec.humor.funny, k...@flash.telesoft.com (Keith Thompson @pulsar) writes: >I really don't understand why the federal government was so slow to >send aid to the areas hit by Hurricane Andrew. After all, both >Florida and Louisiana have oil. That would be funny if it said ``troops'' instead of ``aid''. I wonder if it would still be ``original''. Dan --- Newsgroups: comp.programming, comp.theory, sci.math.num-analysis Followup-To: comp.programming From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 15 Sep 92 17:33:21 GMT Subject: Re: Proving fair shuffles (was: FULL HOUSE) schni...@cs.ucf.edu (Mark Schnitzius) writes: >Assuming you have a true random number generator, is there >a way to _prove_ that a particular algorithm performs an >honest shuffle (i.e. each card has equal possibility of >being in each place)? Are there any order(n) shuffling >routines? Yes, and yes, and the algorithm's in Knuth, and it's faqfully posted here and there (it was in comp.sources.d less than a month ago) possibly because it's a frequently assigned homework exercise. But that still doesn't prevent m...@babar.asd.sgi.com (Michael Jones) from posting the egregious pseudo-shuffle bad> for (card = 0; card < 52; card++) bad> { bad> swap = random() % 52; bad> temp = deck[card]; bad> deck[card] = deck[swap]; bad> deck[swap] = temp; bad> } or ye...@austin.eds.com (Britt Yenne) from misshuffling the first five cards with lossage like bad> for(i = 0; i < 5; i++) bad> { bad> n = random() % 52; bad> s = card[n]; bad> card[n] = card[i]; bad> card[i] = s; bad> } Even d...@messua.informatik.rwth-aachen.de (David Kastrup), offering the good advice to > Use rand/(MAXUNSIGNED/52 + 1) instead of rand%52. doesn't mention that always folding rand to a 52-element range is the commonest, most obvious sign of an incompetent shuffler. But, you may notice, I have not provided a corrected shuffling algorithm! Think of it as an incentive to go read Knuth, or a Pons Asinorum for the lazy student. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: alt.folklore.urban From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 15 Sep 92 22:25:51 GMT Subject: The Craig Conspiracy (Was Re: Credible Evidence?) cro...@math.rutgers.edu (Scott Cromar) writes: > How about we just add Craig to the afu list no matter how it turns > out? Like "Mark Weaver claims to have a snuff film but refused to > show it on request," "Mark Weaver claims to have a snuff film and > showed it to Craig," or whatever. Craig has a point that he'd be > going to an awful lot of work to check out the story. Maybe we'd better consider adding ``Craig Becker'' to the FAQ. If we add ``Craig'' to the FAQ it might be misconstrued. Dan Hoey Hoey@AIC.NRL.Navy.Mil ObUL: The UK has seen a flurry of people changing their name from Shergold to some other name, because they couldn't get mail from overseas. It was being routinely trashed by postal workers who ``knew the story.'' --- Newsgroups: alt.folklore.urban From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 15 Sep 92 22:44:03 GMT Subject: Geek magic (Re: Notorious Toothpaste Skit) st...@emunix.emich.edu (Stewart Tame) writes: > I think that, if this qualifies as magic at all, it's the sort known > as "geek magic." One gentleman I took a closeup class from brought > in a small leghold trap and had it snap on his fingers. We were all > conviced there was a trick to it but he finally persuaded me to try > it. It really didn't hurt that much. I was surprised. The part about geek magic that hurts is taking your prey out of the trap with your teeth. Dan Hoey Hoey@AIC.NRL.Navy.Mil ObUL: ``Nerds'' were originally carnie workers who posed as audience members for the geek show. Their job was to vomit during the show in case the regular audience wasn't sufficiently disgusted. --- Newsgroups: sci.math.num-analysis From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 16 Sep 92 13:58:32 GMT Subject: Re: Prime Number generator Bob.Netherton@dallas.Central.Sun.COM writes: >I would like to run some compute intensive applications as part of some >operating systems tuning research and would like some pointers to some >public domain code for prime number generators and PI calculators using >arbitrarily long integers. Any pointers would be greatly appreciated. If it's not a requirement that the program's output be useless, you could contribute to the network factoring effort. Send email to fac...@src.dec.com, containing a path line of the form path# y...@yourhost.yourdomain or path# host1!...!hostn!you and the line program# and you will receive programs and information, I am told. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: rec.puzzles From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 25 Sep 92 15:37:25 GMT Subject: Re: Factorization puzzle (many more solutions) In response to b...@CS.ColoState.EDU (dave boll)'s puzzle: > Is there an integer whose reverse (written in base 10) contains > exactly the same prime factors as the original number? j...@lentil.princeton.edu (Jaroslaw Tomasz Wroblewski) answers: > One can recycle 2178 here (its reversal is 4 times itself). It is no coincidence that 2178 is a facdrome, a number that is a divisor of its reverse. Every base-ten facdrome has a recycled factorization. I found all the facdromes last year, and you can read about them in the FAQ by mailing "send palintiples" to net...@peregrine.com. (A palintiple is the reverse of a facdrome.) In short, we can characterize the facdromes as follows. For any language L, let PalNLZ(L) denote the set of palindromes over the (infinite) alphabet (L union 0*), except that we exclude from PalNLZ(L) those strings beginning or ending with zero. Then the set of facdromes is the union of PalNLZ(219*78) and PalNLZ(109*89). For example, the following seven numbers are facdromes: 21978, 1089, 1099989, 219978 219978, 10989 0000 10989, 2178 0 21978 21978 0 2178, 10989 1089 000 1089 10989. In addition, I have found some non-facdromes with recycled factorizations. The set PalNLZ(439*56), containing numbers that are two-thirds of their reverse, has this property. Examples include 439956 and 435604356. More interesting is the set PalNLZ(329*67), containing numbers that are three-seventh of their reverse. These numbers have recycled factorizations if and only if they are multiples of seven. Examples include 32999967, 326732673267, 3267000003267, 32967000032967, and 329967000329967. I have not found any other numbers with recycled factorizations, but I would not be surprised if they exist. Also, in bases other than ten, I suspect there may be facdromes that do not have recycled factorizations, but I have not gone looking for them. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: rec.arts.books, rec.arts.comics.strips, rec.arts.sf.written Followup-To: rec.arts.comics.strips Date: 25 Sep 92 21:21:21 GMT From: hoey@aic.nrl.navy.mil (Dan Hoey) Reply-to: sf-lovers-written@Rutgers.Edu Subject: NORB, the book At Magicon I found the collected NORB comic strip by Daniel Pinkwater and Tony Auth. With an introduction by Vonda McIntyre. In case you missed it, this was an attempt to recreate the golden age of Terry and the Pirates and Little Nemo, comics that tell a story instead of just cracking a joke a day. But no one understood. They just thought the strip was trying to make them feel stupid. Daniel Pinkwater said, ``The hate mail was extreme. There was no positive mail at all except two letters, one each from Jules Feiffer and Chaim Potok.'' So it died after 52 weeks, just 312 strips, and they are all collected in this excellent little book. If you have as hard a time finding it as I did, send a SASE to MU Press, 5014-D Roosevelt Way NE, Seattle, WA 98105, and they will send you a free catalog. This book is MUPubs #152, and it retails for $8.95 / 10.95 Canadian, but I don't know what they want for shipping and handling. Dan Hoey Hoey@AIC.NRL.Navy.Mil ``Invasion imminent by space things, now identified as Garkoids. But first, local news...'' --- Newsgroups: sci.math From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 1 Oct 92 14:49:12 GMT Subject: Re: 1, 2, 4, 8, 13...where have I seen it before? chris...@herb-ox.berkeley.edu (chrisman) writes: > I don't know if this sequence has anything to do with > yours, but here it is (an example of a sequence whose > first few terms are misleading): > Let A(n) be the maximum number of regions into which > a circle can be divided by drawing segments between > n points on the circle. > The first few terms are (starting with n=1) > 1, 2, 4, 8, 16, 31 (!). Well, the reason that sequence is so misleading is that A(n)=C(n,0)+C(n,2)+C(n,4), where C(n,k) is the binomial coefficient. It is not hard to prove that A(n) is one (C(n,0)) plus the number of segments (C(n,2)) plus the number of intersecting pairs of segments (C(n,4)). And when you add up alternate pairs of coefficients, you get A[k](n) = C(n,0)+C(n,2)+C(n,4)+...+C(n,2k) = 2^(n-1) for n<=2k, but 2^(n-1)-1 for n=2k+1. Note that Bill Hery's sequence is not of this type. What I found fascinating is that A(10)=256=2^(n-2) (though it turns out that's no coincidence). Are there any other powers of two in the sequence? In any A[k]? Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Article 1025 of rec.arts.sf.fandom: From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Newsgroups: rec.arts.sf.fandom Subject: Beautifle Ohio Conventions in Collision Date: 1 Oct 92 16:46:11 GMT Sender: usenet@ra.nrl.navy.mil Organization: Naval Research Laboratory, Washington, DC Now that we all know the Ohio Valley Filk Fest is going to be in Worthington, OH the weekend of the 23rd, I thought you might be interested in a discovery I made at BSFS last weekend. If you refer to the OVFF vocally, careless listeners may think you're talking about the Out of Body Fan Fund, a service to underwrite the karmic debt of channeling your past lives to today's conventions. Are you ready for Smof-Ra? I'm afraid I'll be at Ditto/Octocon in Cincinnati that weekend, so I won't be able to let the filkers know of this important new discovery. Perhaps word will reach them, somehow. This does seem to be the year for cons in collision, though. Next month Sci-con is opposite Philcon, instead of their usual one week gap. I'll miss the one I miss. It used to be that time was nature's way of keeping everything from happening at once. That's probably breaking down due to global warming and ozone pollution. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: rec.arts.comics.misc From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 5 Oct 92 19:30:26 GMT Subject: Re: HELP, shops in Washington D.C. CARLO...@auvm.american.edu (Carlos Li) writes: >There are a bunch more out in the suburbs, but my comic needs are >simple and I'm too lazy to go too far. If you acquire more complex needs or shed some indolence, the Closet of Comics is worth a trip. I can't speak for its mainstream coverage but its indy selection is impressive. It's on Route 1 in College Park, a couple blocks north of Calvert Road, beside the 'vous, on the east side of the street. Open until 7 except 6 on Sunday. Any other good indy outlets in the burbs? Dan --- Newsgroups: sci.chem From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 5 Oct 92 19:55:39 GMT Subject: Re: Why not mix bleach and ammonia? djcl...@cwis.unomaha.edu (Daniel Jonathan Clute) writes: >I've always been told that a person should NOT mix ammonia and bleach >together; I suppose because chlorine gas is formed. No, I read you get chloramine, which forms dichloramine (explosive), nitrogen trichloride (explosive), and hydrazine (extremely poisonous). If you just want to snort some chlorine, this is overkill. Your vital signs may vary. Don't try this at home. It is a violation of federal law to use these products in a manner inconsistent with their labelling. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: sci.chem From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 6 Oct 92 21:47:48 GMT Subject: Re: H2SO4 + Chlorox??? khartman@fnalc.fnal.gov writes: >Dan, Dan who? Are you responding to Dan Clute's posting or to to my posting? If either, why did you change the subject to H2SO4? We weren't discussing that, we were talking about clorox and ammonia (ammonium hydroxide, NH4OH). >When Sulfuric Acid (H2SO4) and Clorox (Sodium Hypochlorite) are >mixed, Chlorine gas is released. Chlorine is a greenish-yellow gas that >is HIGHLY poisonous, so much so that it was used during World War I for >a poison gas. Chlorine gas is dangerous in high concentration, or if you can't get to fresh air. In the quantities you can release from a few ounces of Clorox, you will more likely cough and run out of the room. You may feel a burning in your mucous membranes for a short time afterwards. I don't advise you to try it, but it's unlikely to inflict permanent damage. >If you read the labels on Chlorine bleach bottles, or kitchen >cleanser cans, you will see a warning about mixing these products >with acids or alkalies, (Drano, Ammonia, etc). Ammonia is very hazardous when mixed with clorox, because it can produce explosive and extremely poisonous compounds. Extremely poisonous as in ``much more dangerous than chlorine.'' Extremely poisonous as in ``you can go blind or die before you know what is happening to you.'' Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: comp.mail.misc, news.admin.misc Followup-To: news.admin.misc From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 6 Oct 92 23:54:34 GMT Subject: Re: Question about unsolicited Internet Email. b...@clarinet.com (Brad Templeton) writes: >Talk about over-reaction. I am quite certain that the number of >annoyed replies and bad publicity they got will be more than enough >to educate and punish them for sending this mail. Glad to hear it. It's wonderful if they get bad publicity over these shenanigans. Maybe the rumors will get around so widely that the next pinhead doesn't even try to send out junk email. But what is the over-reaction? If this sort of thing didn't cause floods of email and postings no one would stop it. t...@Gwinnett.COM (Todd Reese) writes: ]Over-reaction is an understatement. Some people of the net went as far as ]looking up my MX record and threaten me by direct email and also to the ]sysadm's at my feed sites. Good to hear they got your attention. Unfortunately, you just don't get it. ]I am quite upset at the self-righteous attitude of some of the people ]when a simple note to me would have been enough. Don't be upset, just understand them. There are a lot of annoyed people out there, who are just being sure that the incident doesn't go unnoticed. They feel they have a right not to be put on mailing lists in response to their postings, and they want to be sure it gets stopped now and prevented in the future. ]When I found out about it, I did stop everything. Then the HATE mail started ]rolling in. I have taken over the mail box for aba...@gwinnett.com and ]mail in there has reached over 5 Meg. A large return for 1.5 Meg total ]being sent out. About a dozen people of this mail responded by catting the ]man pages back to mail. What a childish reaction! Trying to measure overreaction in terms of volume of junk mail sent versus volume of angry letters plus email bombs is the stupidest argument I've heard today, and that's something. How about measuring number of annoyed people versus number of satisfied people. Sending email bombs is indeed an inexcusable form of network terrorism. Sending notes to feed sites is called raising a stink, and if it raised a big enough stink that people actually fear being disconnected from the net for this sort of idiocy, then that is the desired result. ]They (Abacus) learned of their mistake within a short time. People ]make mistakes in real life every day. Are those people of the net ]faultless?? Take the hate mail to heart. Let Abacus know about it. If you and they think it's overreaction then you and they just don't get it. People write to the net to fulfill their need for communication. They don't expect junk mail in return. The presence of it threatens the usefulness of Usenet as a whole, and must be vigorously suppressed. ``People make mistakes in real life.'' Someone at Abacus made a big mistake in real life. Not with impunity. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: sci.math From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 7 Oct 92 21:09:12 GMT Subject: Re: Irrational? The dictionary (I peeked) says that the Latin word _ratio_ means reason, computation, or reasoning, from which we get the words ratio and reason. I believe that long division was a canonical example of computation, from which come the words having to do with division, and the rest of the words deal with thought process So irrational numbers are numbers you can't get by dividing integers, while irrational people are the ones who can't do the division. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: rec.games.misc, rec.puzzles From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 7 Oct 92 21:25:23 GMT Subject: Re: Wooden "Puzzles"... ch...@mentor.cc.purdue.edu (HCE) writes: >I have a "puzzle" that my grandfather gave me which is a wood >sphere made up of a number of interlocking pieces. You can take it >apart and you have about 10 pieces.... I would really appreciate any >suggestions on where to find such puzzles. There is as mine of information on this type of puzzle in Stewart T. Coffin's book _The_Puzzling_World_of_Polyhedral_Dissections_, part of the Oxford Press Recreations in Math series, ISBN 0-19-286133-6. Nearly 200 pages, over 400 illos and photos. Hundreds of puzzles, and tips on building them yourself. The suppliers they mention are Kadon Enterprises, Inc, 1227 Lorene Dr, Pasadena, MD 21122, USA Pentangle, Over Wallop, Hants SO20 8JA, England Trench Enterprises, Three Cow Green, Bacton, Stowmarket IP14 4HJ, England from whom you may be able to get catalogues. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: rec.humor Followup-To: alt.announce.important.real.important From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 16 Oct 92 14:18:12 GMT Subject: Re: ftp site found har...@engrhub.ucsb.edu (Hahn) writes: >The reason I bother to mention this is that there are >new users out there who should know: >Never fall for any trick that tells you to >enter "your actual user name and password". >In this case it is innoculous, but you should >know never to do such a thing. There are people >who write programs to induce you to enter such information >that, later, they can use to break into your system. There are also new users out there who should know: 1. Be sure to make sure your ladder has its feet on the ground before using it. 2. Do not drive with sun shade in place. 3. Do not strike your video screen with your fist. Use a hammer. This has been a public information announcement. Dan --- Newsgroups: alt.folklore.urban From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 16 Oct 92 22:07:51 GMT Subject: Per O' Possum On the National Radio Company last week, they did a skit called ``cooking with Perot'' in which the putative candidate showed how to cook a possum (or, possibly, how to cook opossum). And when they were done, it tasted just like chicken. ObUL: Ross Perot and Frank Perdue have never been seen at the same time in the same place. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: sci.math, rec.puzzles Followup-To: sci.math From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 16 Oct 92 22:57:12 GMT Subject: Results: Unfolding the tesseract Back in June, orou...@sophia.smith.edu (Joseph O'Rourke) wrote: >Does anyone know how many distinct unfoldings there are of a >hypercube (a 4-dim cube)? I know there are 11 distinct 2-dim >connected shapes that can result from unfolding a (3-dim) cube >[Rucker, "The Fourth Dimension" (1984) p.34]. Well, Rudy Rucker did pass near the topic, but it was covered in somewhat more detail in Martin Gardner's _Mathematical_Carnival_ [1975] article on the hypercube. Gardner mentioned that he posed the question of many ways there are of unfolding a tesseract to _Scientific_American_ readers, and he got so many answers he couldn't decide which (if any) was right. I spent some time this summer counting them. I organized them and counted them by hand, and got 253 cases. Then I reorganized some of them, and noticed some cases I had missed, and now there were 264. Then I wrote a program to count them, and came up with 261; I soon noticed three duplicates in my hand work. Then I compared the program's output with my table, case by case, and they matched. So at this point I am fairly certain there are exactly 261 ways of unfolding the surface of a tesseract into an octocube. (And I am fairly sympathetic with Garder's readers.) Gardner noted that the eleven hexominoes you get by unfolding the surface of a cube: x xxx x xx x xx xx x x xx x x x xxx x xx xx x x xx x xx xx x x x xx x xx xxx xx xx xx x x x xx x x x x x x x x cannot be used to tile a rectangle. I do not know if he tried tiling with the twenty hexominoes you get if you add the reflections of the mirror-asymmetric hexominoes and forbid turning them over. As for the 261 octocubes you get from unfolding a tesseract, were we to build them, it would be infeasible to ``turn them over'' into their mirror images. Therefore we would probably prefer to build a rectangular prism from the 355 octocubes we get by adding mirror images of the 194 mirror-asymmetric octocubes. But I have no plans to check whether that is possible. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: sci.math From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: Thu, 29 Oct 1992 21:15:12 GMT Subject: Re: Infinite Problems m...@cbnewsg.cb.att.com (marc.a.levy) writes: > A road, infinte length, and 1 meter wide needs to be paved. > The thickness of the pavement is given by h= e^-x > This is to be done with 1 cubic meter of pavement.. How?? As infinite-length roads do not exist in our universe, it is clear that your problem does not correspond to a real scenario. But the extent to which your scenario diverges from reality, and the manner of its divergence, is not specified in the problem. So the problem is poorly posed, and we might as well suppose that we will decompose the given stere into unmeasurable sets, and put it back together to form two steres, as in the Banach-Tarski paradox. In some dimensions, I have heard, Banach-Tarski does not allow us to change the volume of our cement. Well enough, then, we can break it into uncountably many points of cement and biject them discontinuously onto any road we care to pave. Too easy. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: news.admin From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 2 Nov 92 14:34:50 GMT Subject: Re: Larry Lippman dealing with jgd@dixie.com After j...@dixie.com (John De Armond) insinuated: >>Yeah, and you see what happened to Larry the Lid too, don't you? ben...@maths.lth.se (Bengt Larsson) protests: >Shut up, John. Larry Lippman is dead. But Bengt, that's exactly what the ``liar and braggart'' DeArmond meant. He suggests that people die who label him what he is. The truth is, of course, that they live on nonetheless. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: rec.arts.disney From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 2 Nov 92 16:21:02 GMT Subject: Re: running a bet l...@po.CWRU.Edu (Linda G. Brashear) writes: >Of course, the "Barbie" doll of Cinderella has her as brunette. I think >she had dark blond/light brown hair, probably. I don't know that you can >go by the way she's portrayed in the parks by the character actress. After >all, they always show her dress as blue, when in the movie it's definitely >white. (Why do they do that? I could understand silver, maybe, but where >do they get blue???) Why it's not white, or even silver, is probably to avoid confusion with Ivory Snow [sic, I know]. Why it's blue is possibly to arouse confusion with the Madonna. No, not the rock star. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: rec.games.abstract From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 12 Nov 92 22:25:51 GMT Subject: Re: Chess on spherical boards. mjd@saul.cis.upenn.edu ("[*] The Power in the Streets") describes turning the chessboard into a sphere by first making the A and H files adjacent to form a cylinder, then > Now pinch the ends together: x,8 (for some letter x) is > orthogonally adjacent to (x+4 mod 8),8 and diagonally to (x+3 mod > 8),8 and (x+5 mod 8),8. and follows up: > Of course this isn't a sphere either, because the circumference > is 8 squares in the east-west direction and 16 squares in the > north-south direction. More to the point, this isn't even topologically a sphere. For instance, it can be covered with disjoint north-south circumferences, but a true sphere cannot be covered with disjoint circles (or homeomorphs thereof). I think topologists would call this a sphere with two cross-caps. The idea of making file x extend into file -x (mod 8) (that is, files a, b, c, and d extend to files h, g, f, and e, respectively) would make the board a sphere. And I like the suggestion of t...@calico.cs.wisc.edu (Brian A. Cole) that we also make rank x extend into rank 1-x (mod 8) (ranks 1, 2, 3, and 4 extend into ranks 8, 7, 6, and 5, respectively) because it emphasizes the symmetry between ranks and files. However, I think Brian's claim that > 1. each square shares one edge each with four other squares. is incorrect, because H4 shares two edges with H5; similarly the other edge centers have only three neighbors. And when he says > 2. moving one square "left" then one square "down" takes you the > same place as moving one square "down" then one square "left" > (and so on for other paths-that-should-go-the-same-place). it should probably be mentioned that whey you go through the "top" or "bottom" the "right" and "left" directions are interchanged, and when you go through a side the "up" and "down" directions are interchanged. (Does this mean that when White pawn at b8 captures f8, it is now moving toward rank 1? How about g8xa8/Q? This has the unusual feature that some bishop paths bounce back when they get to an edge: ...G3,H4,H4,G3,... while others continue on: ...F1,G2,H3,H5,G4,F3,E2,D1,F1,G2,H3,.... Also, a knight on G3 has seven neighbors: F1, H1, H7, H5 (two ways), F5, E4, and E2, and a knight on H4 has seven neighbors: G2, H7, G6 (two ways), G4, F5, and F3. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: rec.games.abstract From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 16 Nov 92 14:27:12 GMT Subject: Re: Twixt - rule correction jon...@nadia.stgt.sub.org (Jonathan Welton) writes: > The descriptions of Twixt posted so far have all been incomplete. > A move consists of 3 parts - > 1. Place a peg in any free hole, > 2. Remove any of your own bridges, > 3. Place bridges between any two of your own pegs which are a knights > move apart. > In parts 2 and 3 you may remove (add) any number of bridges. > Part 2 is the rule that is most often forgotten. Even in the rule books > accompanying some productions of the game it was incorrectly ommitted. I had thought it was possible to remove bridges, too. I guess the problem with the rule books explains why there are ``authorities'' on both sides of the question. > It is an important rule, since it often resolves otherwise drawn > positions. A good example is the mini situation already posted Note that while Jonathan reproduces Felix Lee's flawed mini-situation, he uses an approach that would be possible with the corrected version. X - - ,,O X - - ,,O \ ,'' ,'' - \ O'' X - - O'',X - \ \ => ,,'' \ - X ,,O \ - X'' X ,,O \ - ,'' \ ,'' \ O'' - - X O'' - - X > In fact, with the help of this bridge removal rule, drawn games are > extremely rare in Twixt. But not impossible! Consider the following situation, in which NO bridges have been played, nor are any even immeediately playable! - - - - O - O - - - - - - - - - - O - O - - - - - - - - O - O - - - - - - - - - - O - O - - - - - X - X O X O X - X - X X - X - X O X O X - X - - X - X O X O X - X - X X - X - X O X O X - X - - - - - O - O - - - - - - - - - - O - O - - - - - - - - O - O - - - - - - - - - - O - O - - - - A knight chain must alternate chessboard colors, and there is no way to break through either player's monochromatic monopoly. So neither player can win, even with the cooperation of her opponent. F...@cs.psu.edu (Felix Lee) writes: ] How can we make draws illegal in Twixt? Consider this rule: ] A player is not allowed to make a move that completely blocks off his ] opponent, if the move doesn't win. I don't think this rule will have the desired effect, because the blockage usually happens while some other part of the board is still technically open, but has a double-cross waiting. The blockage would then be playable but the double-cross would thereafter be forbidden! If both players had double-crosses waiting, everyone could spring them except the last player, who need not be the player who created the blockage in the first place. I think the strategy starts to be something like Go's Ko wars. I think it would be an extremely difficult rule to put into practice, because after the blockage was established, you would have to spend part of each turn demonstrating that your opponent ``could'' make a connection across the board, as long as you didn't respond to the various double-crosses. Your strategy would then be to form ever more double-crosses, while springing your opponent's. The loser is the one who is forced to start throwing away moves into uncontested parts of the board while the winner paves an enforced right-of-way. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: rec.puzzles Followup-To: alt.ya.ya.ya.ya From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 18 Nov 92 00:19:51 GMT Subject: Re: Our favorite series var...@meringue.seas.upenn.edu (Kristofor A Varhus) belabors: >Here's everybody's favorite series again: > 1,11,21,1211,111221,... >1. Which is the first term that has a "4" in it? That's in the FAQ, too. >2. Prove your answer to number 1. It's too easy to bother. RTFFAQ. Come back when you have something new. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: rec.games.abstract From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: Wed, 18 Nov 1992 00:40:23 GMT Subject: Re: Sprouts -- a topological game ne...@scs.leeds.ac.uk (Neil Bowers) writes: > One book says sprouts was invented at "Cambridge University a couple of > decades ago". Does anyone have any more details on sprouts? Strategies? It was invented by M.S. Paterson and J.H. Conway. The latter is also known as the inventor of Life and Surreal Numbers. For more information see: Martin Gardner's _Mathematical_Carnival_. Basic stuff from Scientific American from the 70s. Berlekamp, Conway, and Guy's _Winning_Ways_. Does anyone know if they have new sprouts results in the second printing? Applegate, Jacobson, and Sleator's ``Computer Analysis of Sprouts,'' tech report CMU-CS-91-144, available by FTP in file /usr/sleator/public/sprouts.ps.Z on host spade.pc.cs.cmu.edu, 128.2.209.226. Extends winners for misere play up to 9 dots and normal play up to 11 dots. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: rec.arts.disney From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 19 Nov 92 17:45:12 GMT Subject: Re: The Mickey Mouse joke The joke has indeed made the rounds. I understand that if you go to a Disney park in a T-shirt that says, ``I didn't say she was crazy,'' they will will not let you in. Dan --- Newsgroups: rec.arts.comics.misc From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 19 Nov 92 17:57:54 GMT Subject: Re: DC: Superman's death coverage This morning NPR's Morning Edition had a segment on Supercorpse, including excerpts from a song by (if I remember right) Craig Silver. Of course the part I remember went: With his X-ray vision he could see through anyone's clothes But he never abused his privilege, as far as anyone knows. What, never? Dan Hoey@AIC.NRL.Navy.Mil --- Newsgroups: comp.theory From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 27 Nov 92 15:30:45 GMT Subject: Re: Cryptography and P=NP annan@vax.oxford.ac.uk writes: On an ``algorithm'' that halts in polynomial time on accepting a string in a language but may not halt on rejection of a string not in the language. >>>By usual definitions, this is NOT a polynomial time algorithm for the >>>NP-complete language. When I replied: >> On the contrary, by the usual definition cited, this is a polynomial >> time [sic] for recognizing the NP-complete language, as we were discussing. I'm afraid I was mistaken. I was misled by a sentence on on page 25 of Garey and Johnson (to which I was directed by John Mount's message). G&J show a program that does halts on acceptance and does not halt on rejection, and say that the program recognizes the language. But they continue to say that the program ``does not correspond to our notion of an algorithm.'' So there is a *program* that recognizes the language, but not an *algorithm* that recognizes the language. The notion of polynomial time is indeed used to refer to the maximum time taken over all strings over the input alphabet, not just the strings in the recognized language. >What definition do you use? Or are you using "recognising" to mean something >different from "accepting"? Somehow I had gotten the idea that G&J were using the term ``recognizing'' (a language) to refer to a process's behavior on success, while ``deciding'' (membership in a language) referred to the process's behavior on all strings. A more careful reading shows that they make this distinction between a program and an algorithm. I deeply regret having so intemperately rejected James Annan's correct summary of the usual terminology. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: comp.arch From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 27 Nov 92 18:29:18 GMT Subject: Re: Summary: Integers implementation fa...@gr.osf.org (Christian Fabre) writes: >For integers arithmetics, 2's complement is the most >used nowdays with a BIG advantage over 1's complement and >sign-magnitude: only one representation of 0. Another >advantage is that size extension is more [convenient]. Actually, it's more that sign extension makes sense. Which is to say that converting an n-bit twos-complement number to an m-bit number, the low-order min(m,n) bits don't change. So the sign bit does not usually require a lot of extra logic. >1's complement was used (e.g. PDP11, CDC), buts its advantage >of fast negation and symetrical ranges around zero does not >balance the 2 zero problem. The PDP-11 used twos complement. But another use of ones complement is in checksum calculations. I think the advantage is that if you want to find the ones-complement sum of a bunch of n-bit bytes, you can add them up k at a time as a bunch of kn-bit bytes, and then add together the k n-bit bytes in the sum. This saves time when your machine has wide instructions. >sign-magnitude and excess-n are used to represent floating >points number (mantissa and exp, respectively). I'm pretty sure twos complement is often used for the mantissa, too. Excess-n, where n = 2^(# bits - 1), is just twos complement with the top bit complemented. I recall that with a twos complement mantissa and an excess-n exponent, you can use twos complement integer comparisons on floating point numbers. As far as I know, that's the only reason to favor excess-n over twos complement for the exponent. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: comp.dcom.lans.ethernet From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 1 Dec 92 18:53:29 GMT Subject: Reliability (?) of Cabletron MT-800 Multiport XCeiver The Cabletron MT-800 is my favorite Ethernet concentrator, largely for its collection of LEDs that give me an idea of what's up with the lan. But in the past year four of our MT-800s have toasted their power supplies, out of a population of about twenty. Are we just having an unlucky year, or is this unit suicide-prone? Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: alt.folklore.computers, news.admin.misc From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: Tue, 1 Dec 1992 21:42:22 GMT Subject: Re: Famous flame wars, examples please? aiken!d40...@vlsi.polymtl.ca (Jean Yves Desbiens) writes: >I would like to know if there has been in the past some >celebrated flame wars in the past? Numerous people mention newsgroup naming wars, and wo...@wolves.Durham.NC.US (G. Wolfe Woodbury) said > Well, the "first" flame war on "Usenet" took place even before it > had a real name .... Well, before there was Usenet and Internet, there was Arpanet. The first flame war I know of was on an Arpanet mailing list called HEADER-PEOPLE, a distant ancestor of comp.mail.headers. I believe the year was 1979. Back then you could have addresses like "Joe R. Schmo@Somewhere" where the spaces and punctuation were part of the address. This was written up in RFC-733 and was a standard. Some system, I think it was Tenex, was storing outgoing mail in files named by the address, and they suddenly realized their system wouldn't let them put spaces in file names. So they asked the Arpanet managers to make the spaces go away, and there was suddenly an order thundered down to the network that addresses with spaces in them were ``no longer standard.'' The people who had spent several years putting together the mail standards didn't think that standards should be modified to conform to the bugs in implementations, and sent several hundred angry messages back and forth on the subject for a week or two. In the end, they couldn't do anything about it except refuse to modify their mail systems. But then it was their systems that were ``nonstandard,'' and nobody could use addresses with spaces in them because nobody could send them mail. Eventually they all got ``fixed.'' Or, like Tenex, they got left on the ash-heap of history. This is the first time I'm aware of that a network argument was called ``flaming.'' Cooler heads told people to calm down and start acting civilized. I'm pretty sure they were shouted down. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: rec.games.abstract From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 2 Dec 92 22:42:22 GMT Subject: Poison Cookie, Moldy Chocolate, and Chomp (was Gale's Game) m...@saul.cis.upenn.edu (Jasper Titus) described Gale's game, or Chomp: > 1. Choose integers M and N to be the size of your board. > 2. A legal move is a choice of integers (p, q), with 1<=p<=M > and 1<=q<=N, and such that there's no previous move (x, y) > with (x<=p and y<=q). > 3. If you play (1, 1), you lose. d...@doc.ic.ac.uk (Denis Howe) writes: > It is a special case of Poison Cookie where, if I remember rightly, > one square of a rectangular grid (the cookie) is marked as poison and > the players alternate taking rectangular bites *from any direction* > until the last one loses when he has to eat the poison. I can't > remember if a bite had to include a corner or if you could nibble in > from a side. I have never heard of this Poison Cookie before. Is it published? At first I thought you were talking about Moldy Chocolate (as in Ian Watson's _Another_Fine_Math_You've_Got_Me_Into..._) in which players alternate taking half-planes away from the rectangular grid of chocolate, trying to avoid taking the moldy piece. This turns out to be quite an easy game once you penetrate its disguise. Watson describes Moldy Chocolate only with the simplifying assumption that the moldy piece is at the corner of the rectangular field, which makes the game so simple that you might not see the disguise. I've only seen Chomp described with the poison square at the corner and the bites taken out from the opposite direction. This saves us from having to deal with cases like | . C C C C C . . . . .|C . . . . . C . C C C C C . . . . .|C . . . ._._C_ . C C C C C . . . . .|C . . .|. . . . C C C C C => _._._._._.|C => . . .|. . . . . P C C C . . P C C C . . P|. . . . . . C C C . . . C C C . . .|. . . | in which the poison becomes separated from the rest of the game. Of course Poison Cookie could be at least this strange, depending on what is allowed and what isn't. Though from the description of ``rectangular bites'' it's not clear you can make these moves all at once, or whether you are required to take intact rectangles, as in _______ . C C C C C .|. . . .|C . . . . . C . . . . . C . C C C C C .|. . . .|C . . . . . C . . . . . C . C C C C C .|. . . .|C . . . . . C . . . . .|.| . C C C C C => .|._._._.|C => . . . ._._C => . . . . .|.| . . P C C C . . P C C C . . P|. . .| . . P . . . . . . C C C . . . C C C . . .|._._.| . . . . . . f...@cs.psu.edu (Felix Lee) writes: > Winning Ways also gives a related game: Given a number N, players > take turns naming divisors of N which may not be multiples of > previously named divisors. Whoever names 1 loses. At least in the 1st printing of _W_W_, this is the only form of Chomp described. That's unfortunate, because it doesn't lend itself to the infinite analogue, in which you start with an infinite quarter-plane of chocolate (an especially attractive game to those of us who like to imagine an infinite quarter-plane of chocolate). It does, however, lead immediately to the higher-dimensional analogues, in which the number N may have three or more prime divisors. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: comp.dcom.lans.ethernet From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 4 Dec 92 17:49:59 GMT Subject: Unreliability of Cabletron MT-800 Multiport XCeiver, summary I asked: >The Cabletron MT-800 is my favorite Ethernet concentrator, largely >for its collection of LEDs that give me an idea of what's up with the >lan. But in the past year four of our MT-800s have toasted their >power supplies, out of a population of about twenty.... I got six similar horror stories, including someone who got a couple of toasted MT-800's at a swap meet and wanted to know what the supply is supposed to output (I think +5V and +13V). The most favorable report was from someone who fried four last year but none this year. (I wonder if it could be traffic-dependent. My net does have a lot more collisions than it ought to). Oh, and Cabletron's other stuff seems all right, just this one seems a little flakey. Much thanks to Randy Meyers, who recommended a MPX with LEDS from Optical Data Systems 1101 E. Arapaho Rd. Richardson, TX 75081 (214)301-3600 h...@ods.com Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: comp.lang.c From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 6 Dec 92 23:14:01 GMT Subject: Re: C palindrome puzzle With regard to the code: /**/ #include main() { printf("Hello world.\n"); } /*/ } ;)"n\.dlrow olleH"(ftnirp { )(niam >h.oidts< edulcni# /**/ bl...@kastle.Princeton.EDU (Matthias Blume) writes: > This raises another interesting question: > Not counting whitespace, can it be done with an even number of characters? scjo...@thor.sdrc.com (Larry Jones) responds >Sure, just replace the middle line with "/**/" -- the center section can >be anything you want as long as it starts with "/*" and is palindromic. Wrong. If it contains "*/" after the last "/*" (as your example does) it will not succeed in commenting the nonsense section that follows, and the program will fail. However, it is possible to replace the middle line with "/*//**//*/". Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: dc.general From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 8 Dec 92 23:31:19 GMT Subject: Re: Evecon (was Re: Needed - Ideas for...) r...@access.digex.com (Richard L. Butler) wrote: >For those who believe that it is evil to make money from fannish >activities, I believe that both of the FanTek cons (they also do >CastleCon in the summer) are run on a for-profit basis by Bruce. >Be warned, or grow up. elec...@access.digex.com (Gary Ehrlich) replied: >Mainly on the basis that they dream of building a castle somewhere in >the DC/MD/VA area someday. Whether they've actually made monetary >progress towards that goal, I couldn't tell you It's hard to argue about what they dream of. The basis I heard was that the profits were used as personal income, for supporting living expenses. Arguably, people have better dreams with an income. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: comp.std.c From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 9 Dec 92 19:09:39 GMT Subject: Re: mathematical modulo operation geo...@cs.tut.fi (Campbell George) writes: >Is this implementation of the modulo function guaranteed [to work?] >int mod(int j,int N) {return((((j)%N) < 0) ? ((j) % N)+N : ((j) % N));} diam...@jit.dec.com (Norman Diamond) writes: >Strictly speaking, the implementation is free to define which of two >allowed results is produced for % when the divisor is negative. I >don't know any implementation where the implementation definition >might say that the result alternates from one invocation to the next, >but it's not clear if the standard allows it. Doesn't the standard require that quotient and modulo be consistent, so that (j/N)*N + j%N == N ? I think this pretty much requires modulo to return the same value every time, at least throughout a single execution of the program. I suppose the compiler _might_ be able to figure out that your program never takes the quotient of those particular numbers, so that it has nothing to be consistent with.... Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: misc.misc, misc.writing, rec.misc Followup-To: misc.misc From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 9 Dec 92 21:21:32 GMT Subject: Re: Looking for list of PALINDROMES... jejen...@alfred.carleton.ca (John Jensen) writes: >Hello, I'm looking for an electronic list of palindromes (eg. "A man, >a plan, a canal: Panama"). I have seen one floating around the net >but my search has thus far been fruitless. Can anyone help? Here is some information about a few palindromes related to the one you mention. As far as I know, the first person to put a cat in the canal was Jim Saxe, in his 9 October 1983 plan file. A man, a plan, a cat, a canal; Panama? Guy Jacobson added several items later that year. A man, a plan, a cat, a ham, a yak, a yam, a hat, a canal--Panama! Guy's palindrome appears on page 127 of COMMON LISP, THE LANGUAGE (page 170 of the 2nd edition). The 2nd edition of COMMON LISP, THE LANGUAGE also contains the remarkable: A man, a plan, a canoe, pasta, heros, rajahs, a coloratura, maps, snipe, percale, macaroni, a gag, a banana bag, a tan, a tag, a banana bag again (or a camel), a crepe, pins, Spam, a rut, a Rolo, cash, a jar, sore hats, a peon, a canal--Panama! which is presumably the work of Guy Steele, the book's author. I dredged up the problem in 1984, and discovered the following 540-word version with the help of a computer program that I wrote. A man, a plan, a caret, a ban, a myriad, a sum, a lac, a liar, a hoop, a pint, a catalpa, a gas, an oil, a bird, a yell, a vat, a caw, a pax, a wag, a tax, a nay, a ram, a cap, a yam, a gay, a tsar, a wall, a car, a luger, a ward, a bin, a woman, a vassal, a wolf, a tuna, a nit, a pall, a fret, a watt, a bay, a daub, a tan, a cab, a datum, a gall, a hat, a fag, a zap, a say, a jaw, a lay, a wet, a gallop, a tug, a trot, a trap, a tram, a torr, a caper, a top, a tonk, a toll, a ball, a fair, a sax, a minim, a tenor, a bass, a passer, a capital, a rut, an amen, a ted, a cabal, a tang, a sun, an ass, a maw, a sag, a jam, a dam, a sub, a salt, an axon, a sail, an ad, a wadi, a radian, a room, a rood, a rip, a tad, a pariah, a revel, a reel, a reed, a pool, a plug, a pin, a peek, a parabola, a dog, a pat, a cud, a nu, a fan, a pal, a rum, a nod, an eta, a lag, an eel, a batik, a mug, a mot, a nap, a maxim, a mood, a leek, a grub, a gob, a gel, a drab, a citadel, a total, a cedar, a tap, a gag, a rat, a manor, a bar, a gal, a cola, a pap, a yaw, a tab, a raj, a gab, a nag, a pagan, a bag, a jar, a bat, a way, a papa, a local, a gar, a baron, a mat, a rag, a gap, a tar, a decal, a tot, a led, a tic, a bard, a leg, a bog, a burg, a keel, a doom, a mix, a map, an atom, a gum, a kit, a baleen, a gala, a ten, a don, a mural, a pan, a faun, a ducat, a pagoda, a lob, a rap, a keep, a nip, a gulp, a loop, a deer, a leer, a lever, a hair, a pad, a tapir, a door, a moor, an aid, a raid, a wad, an alias, an ox, an atlas, a bus, a madam, a jag, a saw, a mass, an anus, a gnat, a lab, a cadet, an em, a natural, a tip, a caress, a pass, a baronet, a minimax, a sari, a fall, a ballot, a knot, a pot, a rep, a carrot, a mart, a part, a tort, a gut, a poll, a gateway, a law, a jay, a sap, a zag, a fat, a hall, a gamut, a dab, a can, a tabu, a day, a batt, a waterfall, a patina, a nut, a flow, a lass, a van, a mow, a nib, a draw, a regular, a call, a war, a stay, a gam, a yap, a cam, a ray, an ax, a tag, a wax, a paw, a cat, a valley, a drib, a lion, a saga, a plat, a catnip, a pooh, a rail, a calamus, a dairyman, a bater, a canal--Panama. This was done with the Unix spelling dictionary and a fairly simple-minded program. With a better word list and a smarter program I'm sure the palindrome could be ten times as long. I am somewhat concerned that people have been redistributing these palindromes without attribution. Please don't do so. And if you get a copy of my palindrome without my name on it, I would appreciate it if you mention my objection to whoever sends it to you. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: comp.lang.c From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 9 Dec 92 21:40:11 GMT Subject: Re: C palindrome puzzle vo...@crd.ge.com (Chris Volpe) writes: >Or better yet, a self-replicating palindrome? I thought you'd never ask. Here's one I wrote in 1987: /**/main(){char*a=/*/};)q,q,a,q,q,811+a(ftnirp;'"'=q,/**/" /**/main(){char*a=/*/};)q,q,a,q,q,811+a(ftnirp;'c%'=q,/**/c% s%c%/**/,q='c%';printf(a+118,q,q,a,q,q);}/*/=a*rahc{)(niam/* */main(){char*a=/*/};)q,q,a,q,q,811+a(ftnirp;'%c'=q,/**/%c%s %c/**/,q='%c';printf(a+118,q,q,a,q,q);}/*/=a*rahc{)(niam/**/ "/**/,q='"';printf(a+118,q,q,a,q,q);}/*/=a*rahc{)(niam/**/ It doesn't really have any newlines in it, I've just written it that way to make it easier to read and mail. If you wanted it to #include or have newlines it would be longer and less symmetric, but it could be done. If you wanted to use 32 for '"' it would be shorter but morally inferior. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: comp.lang.c From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 10 Dec 92 23:27:25 GMT Subject: Re: How to do an efficient ROTATE in C? mo...@thunder.mcrcim.mcgill.edu (der Mouse) writes: >raym...@kronos.arc.nasa.gov (Eric A. Raymond) writes: >> C has those lovely >> and << ops for shifting, but no built in rotate >> operators? I generally use (val<>(wordsize-shift))&((1<> Why isn't this part of the language? Perhaps it's not a common >> instruction on many CPU's? >Perhaps because the PDP-11 model(s) used when developing C didn't >have it? I'm pretty sure it was in the original PDP11 instruction set. >Some models do, but I don't know how widespread it is, and the >ones that do have it rotate by only one bit, through the carry, which >makes it hard to represent in C. I'm sure anything in C would be a 16-bit or 8-bit rotate not involving the carry. For a multiple bit rotate left, you clear the carry, then repeatedly rotate left and add the carry. For a multiple bit rotate right, you can either simulate with a complementary rotate left, or you can duplicate the quantity to be rotated, then alternately rotate the scratch copy and rotate the good copy. The scratch copy is just used to set the carry bit. >> Perhaps it's not that commonly needed as shift? One thing is that it's relatively more dependent on word size than shift. A signed shift doesn't depend on the word size unless it overflows. But that's more applicable to a language like Lisp, where you treat integers as unbounded bit strings (with all but finitely many of the bits zero or one). Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: rec.arts.movies From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 11 Dec 92 19:50:24 GMT Subject: Re: want info on THE LOVER actress c...@gsbux1.uchicago.edu (Cal Lott) writes: >There was a minor controversy over the supposed age of the >*character* in the move, not the age of Ms. March. In a piece of >dialogue where Leung's character asks her how old she is, she replies >"fifteen" in the original cut of the movie. When the movie was >released in the U.S.A., >the dialogue had to be changed to "eighteen".... That's close, but not quite what I read in the DC City Paper (which has been known to get things wrong, but...) According to their review, the young girl says eighteen but the narrator--her older self--says that it was a lie. It was the narrator's correction that was excised. Having never seen the uncut version, I can't say which account is accurate. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: rec.games.abstract From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: Wed, 16 Dec 1992 16:54:02 GMT Subject: Re: Sid Sackson paper-and-pencil(s) games I found Sid Sackson's book _A_Gamut_of_Games_ in a used book store last month, and I've been meaning to mention it to this group. Unfortunately, I don't have it with me at the moment, but I'll tell what I can from memory. It has a lot of games, mostly by Sackson but also by other authors. Most are many-player games (which I tend to avoid because of the coalition dilemmata) or word games (generally either non-abstract or intrinsically having a huge ``supplementary rule book'') but there are a few classic two-player games. Also the book has a review section describing about a hundred games. Lots of Avalon Hills, a review of the game of Life (No, not the Conway cellular automaton, the commercial N-player chase game), two versions of Par*ch[ei]*si, three versions of Qubic, and several of the Wff'N'Proof series. It mentions that Sackson headed the New York Games Federation (or some approximation of that name). I wonder if that organization (or any similar ones) still exist? One game I remember (but not its name) because it is a classic unimpartial game and might yield to some study. The board is a rectangular array of points. Players take turns drawing a straight line from one point to another, possibly going through other points. No line may intersect a previous line, even at an endpoint. It is explicitly mentioned that oblique lines are allowed, but it is _not_ made clear whether oblique lines are restricted to forty-five degree angles. I prefer to extend this to three versions of the game: n.o.l., r.o.l., and u.o.l., in which oblique lines are respectively not allowed, restricted, and unrestricted. In normal play (last player to move wins), an obvious first-player win exists in the r.o.l. and u.o.l. versions, and in the n.o.l. version on all boards with an odd side. The second player wins normal play n.o.l. on 2Nx2M boards. (If the reader cannot do these exercises, I suggest he request the solution by email; I discourage posted spoilers to this trivial problem (of which I may revise my opinion if I get a lot of email requests.)) Does anyone care to analyze the misere version? Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: news.software.nntp, news.misc Followup-To: news.software.nntp From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 16 Dec 92 18:59:38 GMT Subject: Found Humor (was Re: Are Message-IDs case significant ?) henry@zoo.toronto.edu (Henry Spencer) writes: HS: gritton@byu.edu writes: HS: >> There are some 822 constructs which would cause exceptions to this, but HS: >> they are extremely rare, and I know of no existing news system which HS: >> attempts to implement them. [I omit the rest of Henry's message -- DH] First, for people who aren't accustomed to parsing brockets, I should point out that the quoted text appears to be Henry Spencer's own (from article , in case anyone cares.) And second, I can't help expressing my awe at the statement, perhaps the most amusingly amazing quotation out of context that I have ever seen on Usenet. It ought to win an award. On closer examination, I found that Henry was referring to _RFC_ 822. Dan Hoey@AIC.NRL.Navy.Mil --- Newsgroups: sci.math.symbolic, sci.math, alt.uu.math.misc, misc.forsale Followup-To: misc.forsale From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 16 Dec 92 22:17:23 GMT Subject: More lies and abuses from Weiguang Huang (was SIMTEL-20 symbolic...) When Charles Yeomans suggested that Weiguang Huang's advertisements constituted commercial use of the net, Huang replied: > I don't think so. Because I answered the question about SIMTEL20 > software posted by Li and SymbMath is not commerical. There are four reasons I don't believe that reply. First, Li asked how to get software from SIMTEL-20. Huang's post did not answer the question, it only told how to get Symbmath, not any of the other software on SIMTEL-20. Second, Li requested a response by email. Not only did Huang post his reply to the net, he added three other newsgroups in which the question had not been asked. That is not answering the question, it is advertising. Third, Li asked the question eight days before Huang answered it. That is a little odd. Usually, after a week the question has been answered and there's no reason to answer it any more. I suspect Huang was only looking for an excuse to post his advertisement. But that eight-day gap is relatively mild by Huang's standards. Last week he posted an advertisement that was putatively in response to a request for information posted in August! Does anyone think he's concerned that someone might have been waiting for his advertisement for three months? And on that one, he added four newsgroups that the question wasn't asked on. And he included the 30-line product announcement he posted to seven newsgroups less than two weeks earlier. Of course, just in case your system might accidentally drop these gems, he puts a six-month expiration date on them. Go hire a billboard, Huang. Fourth, Huang says Symbmath is not commercial. That is an outright lie. The version available through FTP is the type of commercial software misleadingly called ``shareware'', in which people are permitted to use the software for free to see if it is useful to them, but are required to pay money for continued use of the software. Shareware is commercial software, it just relies on the honesty of the user to collect the money. And just in case anyone might be tempted to use the shareware version of Symbmath without paying for it, Huang has crippled it by taking out all but the most trivial uses. If you want to do anything real with it, you'd better be prepared to pay up front for the expensive version. Huang's repeated, verbose, intentionally deceptive advertisements are _precisely_ why advertising on the network is a bad thing. If you want to spend your news reading time wading through ads from every parasite who thinks they can make a buck off Usenet readers, then sending money to Huang is a great way of encouraging it. In light of this, Huang's accusation of commercial use by Kate Atherley of Maple Technical Support is a pathetic slander. She responded to a question asking which version of Maple would run on a PC, and she answered it promptly and concisely, with a phone number and net address in case anyone wanted to go looking for more details or a sales pitch. There are newsgroups in which advertisments are permitted, even encouraged. One such is misc.forsale, to which I have directed followups to this message. Take the ads away from sci.math, sci.math.symbolic, and all the other newsgroups in which advertisements are not welcome. Dan Hoey Hoey@AIC.NRL.Navy.Mil [ In case anyone cares, I don't use Symbmath or Maple. I occasionally use Mathematica, and I used to use Macsyma. I have no connection with any of the companies that make symbolic mathematics software. But I read Usenet news, and I don't want to have to wade through ads from every advertiser who thinks they can make money off of readers of a particular newsgroup. This post is an attempt to discourage advertisers from posting ads to noncommercial newsgroups. It is not enough to ignore Huang, because his abuse of Usenet welcomes other parasites in these and other groups. ] --- Newsgroups: rec.games.abstract From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: Thu, 17 Dec 1992 16:45:02 GMT Subject: Re: Sid Sackson, corrections Yesterday I wrote about Sid Sackson's 1969 book _A_Gamut_of_Games_ from memory. From looking in the book (``You can observe a lot just by watching.'' Stengel or Berra?) I've got a few additions and corrections. He got Martin Gardner to write some pretty ripe cover blurbs, calling Sackson ``the country's leading game inventor, collector, and expert on game history'' and _Gamut_ ``the most important book on games to appear in decades.'' Personally, I think Gardner is being too modest about his own books. The organization that Sackson was president of is called ``New York Game Associates.'' While I had assumed it was a fan club, I suppose it could be a trade association or a private company. Does anyone know what it was, or what's become of it? I pretty badly misremembered the game ``Hold That Line'' yesterday. I was right about board being a rectangular array of points, and players take turns drawing a straight line from one point to another, possibly going through other points. The difference is that each line but the first must share just one endpoint with the path formed by the previous lines. No line may otherwise intersect a previous line, even at an endpoint. Play continues until no more moves are possible. As I mentioned, oblique lines are allowed, but it is _not_ made clear whether oblique lines are restricted to forty-five degree angles. I extend this to three versions of the game: n.o.l., r.o.l., and u.o.l., in which oblique lines are respectively not allowed, restricted, and unrestricted. I was right that in normal play (last player to move wins), an obvious first-player win exists in the r.o.l. and u.o.l. versions, and in the n.o.l. version on all boards with an odd side (if you don't see how send email; if you do don't spoil it), but I do not know who wins in normal play n.o.l. on 2Nx2M boards. Are there any takers on this last problem, or on the misere version? Sackson apparently noticed that the misere version is the hard one, for he says ``the player who was forced to make the last line is the loser!'' Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: comp.theory From: hoey@zogwarg.etl.army.mil (Dan Hoey) Date: 23 Dec 92 18:45:31 GMT Subject: Re: Real Numbers vs. Rational Numbers? dider...@di.epfl.ch (Claude Diderich) writes: >I asked myself some time ago the same question (e.g. are Turing >machines computing on real numbers equvalent on ones computing only >on rationals), but I was unable to find any answer. I was especially >intersted in complexity theoretical results. One interesting complexity non-result is the open question: Is the travelling salesman problem with cities on an integer lattice in NP? The numbers are non only real, but algebraic. Not only algebraic, but constructible! Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: alt.folklore.urban From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: Thu, 24 Dec 1992 17:18:08 GMT Subject: Re: Mnemonics It's hard to tell who first wrote >>I have never learned the mnemonic "thirty days hath September.....". but if you want to know how many _nights_ there are a month, you can use this mnemonic by Justin Richardson from _The_Faber_Book_of_ _Useful_Verse_ (Simon Brett, ed.) Rhyme for Remembering How Many Nights There are in the Month Thirty-one nights hath December, Plus six others we remember-- Jan., July, Aug., May, Mar., Oct. The rest to thirty nights are docked, Save Feb., which twenty-nine hath clear, And twenty-eight each un-leap year. If only my grandfather had known this. He performed laborious calculations in biblical numerology, using 365.25 days per year and 365 nights. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: alt.folklore.urban From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: Thu, 24 Dec 1992 19:19:15 GMT Subject: Re: Dead Cat r...@hpfcso.FC.HP.COM (Ray Depew) writes: > ... I heard it from a friend of ours, at a party. One. > I've never known her to lie, Two. > and for all I know, it really did happen. Three. > In any case, it was a great story,.... Four. I was told there was a prize for most AFU slogans in succession. > Aunt and cousin got inside the mall just in time to see the guy stop and open > the bag for a look inside. When he saw what was in the bag, he dropped it > and fainted dead away. Hit his head on the hard tile floor, too. Out cold. > Somebody called 911, and soon an ambulance crew came rushing in. They > checked the poor guy, and decided to haul him to the hospital. So they > gently put him on the gurney, placed his shopping bag on his chest, and > wheeled him out. End of story. > Well? Well, you left out the last part of the story, where the AACOAF tell the ambulance crew what happened, and the crew breaks out laughing so hard they drop the patient, breaking his leg. Then there's an optional last verse about how after he recovers he sues the ambulance crew, the aunt, the cousin, the mall, and the manufacturer of the bag for battery and cruelty and wrongful surprise and misuse of a corpse. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: comp.theory From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: Mon, 28 Dec 1992 16:24:49 GMT Subject: Re: Real Numbers vs. Rational Numbers? I wrote: >One interesting complexity non-result is the open question: > Is the travelling salesman problem with cities on an integer > lattice in NP? >The numbers are non only real, but algebraic. Not only algebraic, but >constructible! And djime...@ringer.cs.utsa.edu (Daniel Jimenez) replied: > Hmm. I think you mean P, not NP (obviously it's in NP). No, I meant NP. And it is sufficiently nonobvious to be a decades-old open problem. The hard part about showing this is in NP is the problem of finding which of two candidate tours is shorter. In particular, the problem Given two sets {a1, ..., an} and {b1, ..., bn} of positive integers, determine whether sqrt(a1)+sqrt(a2)+...+sqrt(an) > sqrt(b1)+sqrt(b2)+...+sqrt(bn) is not known to be in NP or co-NP. If you have any good way of showing how a NDTM can determine that question in polynomial time, you should publish it. You may, if you wish, provide a method that only works when each of the ai and bi is the sum of two squares. (If that helps, the result will be even more amazing.) > Anyway, it seems like this problem is NP-complete.... It is well known as an NP-hard problem. In fact, given n points in the integer lattice, the question of whether there exists a Hamiltonian circuit of length n--i.e., consisting of unit-length edges--is known to be NP-complete. This is how it is shown that Euclidean TSP is NP-complete. I don't have it with me, but I believe you will find all of this in _The_Traveling_Salesman_Problem_, Lawler et. al. (Eds.), Wiley, '85. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: alt.folklore.urban From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: Thu, 31 Dec 1992 21:02:12 GMT Subject: Re: Roach hotel sas...@jjoyce.unx.sas.com (Bruce Tindall) writes: >This brings to mind a real UL about a hotel in Charleston, S.C.,.... > [bulk deleted] >She was placated, until she noticed a little piece of paper still in >the envelope. Apparently a note from the manager to his secretary, >it said, "Send this old bag the Roach Letter." A related story appears in P. G. Wodehouse's 1910 novel _Psmith_in_ _the_City_. After his friend is fired in the presence of a customer, Psmith suggests the firing may have been for show: ``In America, as possibly you are aware, there is a regular post of mistake-clerk, whose duty it is to receive in the neck anything that happens to be coming along when customers make complaints. He is hauled into the presence of the foaming customer, cursed, and sacked. The customer goes away appeased. The mistake-clerk, if the harangue has been unusually energetic, applies for a rise of salary.'' Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: alt.folklore.urban From: hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: Thu, 31 Dec 1992 22:42:33 GMT Subject: Re: Licking the bars jonat...@vort.cuc.ab.ca (Jonathan Levine) writes: > Getting your tongue frozen to a piece of metal outdoors in the > winter is comonly known as "licking the bars". The origin is > schoolchildren, as the bars referred to are those comprising the > fence around the schoolyard. A kid I knew in high school claimed to have done this, but I had a hard time believing he was that stupid. I suspected he was using it as a cover story for lesions due to some even more embarrassing stunt but I couldn't imagine what it could possibly be. But it does happen, according to an article I read earlier this very winter, probably in Harper's. This story had a happy ending, though, because the child's father was there, and thinking quickly, freed the child's tongue with only minor damage by urinating on it. The doctor commended his quick thinking. The kid was not available for comment. > BTW, how widespread is knowledge of "the dogpile"? They soothe them by licking, too. Dog saliva is reputed to have enormous healing powers and dogs' tongues reach places you and I can only imagine. Dan Hoey Hoey@AIC.NRL.Navy.Mil ---