Newsgroups: rec.puzzles
From: Hoey@AIC.NRL.Navy.Mil (Dan Hoey)
Date: 1997/12/15
Subject: Re: How many points (9 different queens...)

se...@panix.com (Seth Breidbart) writes:

About putting the maximum number of nonattacking queens on a
chessboard, in the presence of extra wood for blocking:

> OK, here's the proof:

> Say that a queen poisons the square it's on, and the squares directly
> to its right, above it, and diagonally above right.  Now each queen
> poisons 4 squares, and no square can be poisoned by more than one
> queen, so 16 is an upper bound.

Bogus proof.  Some of those poisoned squares you're counting may not
exist.

A good proof is to divide the board into 16 2x2 blocks.  There can be
at most one queen per block (it poisons the rest of the block, if you
like) yielding the bound.

ObPuzzle:  Give a neat proof for at most 32 pawns, 24 if we exclude
ranks 1 and 8.

Dan Hoey
Hoey@AIC.NRL.Navy.Mil                posted and e-mailed