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From: Bruce Stephens <bruce@liverpool.ac.uk>
Subject: Re: Nudge, please:  Magic Toyshop
In-Reply-To: rad@crl.com's message of 13 Oct 1995 13:51:11 -0700
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References: <65016.mamster@pomona.edu> <45mjfv$1m8@crl7.crl.com>
Date: Tue, 24 Oct 1995 10:55:43 GMT
Lines: 29

>>>>> "Robert" == Robert A DeLisle <rad@crl.com> writes:

> Matthew Amster (mamster@pomona.edu) wrote:
>> The lines-and-boxes puzzle, to be precise.

>> I solved tic-tac-toe with no trouble, but this one's tougher.  I
>> suspect I need to either convince Catharine to go first or I should
>> pass at some point in the game.  I cannot figure out how to do
>> either of these things.  Am I on the right track?

> No.  This is a fair game.  Choose the correct lines and you win.  I
> think the author spoiled the game by requiring cheating in some
> puzzles, but not in others.  This has misled several players.  I
> would prefer not to cheat.  I like the idea and Catharine.

A complete analysis is given in "Winning Ways", available from any
University library.

Essentially it's a question of symmetry: watch how Catharine plays,
and see if you can foil her.

Alternatively, do what I did and write a brute force program to give
you an optimal move from any position.  The game is small enough for
that to be quite practical.
-- 
Bruce                   Institute of Advanced Scientific Computation
bruce@liverpool.ac.uk   University of Liverpool
http://supr.scm.liv.ac.uk/~bruce/

