Newsgroups: rec.puzzles, sci.math
From: Dan Hoey <haoyuep@aol.com>
Date: Tue, 30 Sep 2008 17:42:43 -0400
Subject: Re: Wind Around Solitaire

Leroy Quet wrote:
> Here is a 1-player game played on an n-by-n grid, where n is odd. (I
> suggest an n of about 13 to 21 for beginners.)

> The player places the numbers 1,2,3,...n^2 into the grid.

> 1 goes in the center square.

> Each number (2k+1) must go either below, above, left of, or right of
> the square with (2k-1) in it.

> Each number (2k) can go anywhere in the grid.

> Numbers can only be placed in empty squares.

> The player's score is the number of times the path of odd integers
> goes completely around the center square clockwise before the player
> is unable to place any more numbers in the grid.

Why should we count only the odd integers in the path?

What happens when one segment of the path passes through the center
point?  It should probably count as 1/2 of a circle, but is it
clockwise or counterclockwise?

Perhaps we should count how many times the path goes around a point
P=((n+1+e)/2, (n+1+e^2)/2), where e is a positive number small enough
that no line between two grid points contains P.  I think e=1/n is
small enough.

Dan Hoey
haoyuep@aol.com