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Path: utzoo!linus!faron!meister
From: meister@faron.UUCP (Philip W. Servita)
Newsgroups: net.puzzle
Subject: Re: pennies puzzle
Message-ID: <480@faron.UUCP>
Date: Wed, 19-Feb-86 11:12:17 EST
Article-I.D.: faron.480
Posted: Wed Feb 19 11:12:17 1986
Date-Received: Thu, 20-Feb-86 00:04:51 EST
References: <953@houxa.UUCP>
Reply-To: meister@faron.UUCP (Philip W. Servita)
Organization: The MITRE Coporation, Bedford, MA
Lines: 35

In article <953@houxa.UUCP> qts@houxa.UUCP (J.RAMMING) writes:
>Imagine a two-player game, in which each of the players begins
>with an infinite number of pennies.  There exists a round table,
>and each player in his turn places a penny on the table.  (Turns
>are alternated).  The game ends when there is no more room on the
>table for any pennies.  The person who last put a penny on the table
>is declared the winner.
>
>Question:  Given that one of these players has a winning strategy,
>   	which player (the first, or the second) can always win?  
>	Prove your answer by giving the strategy.

First player win. The general strategy is simple: label the center of the 
table the origin, and, assuming you are the second player, and the first player
just made a move M to (x,y), just make your move to (-x,-y). in this fashion 
there will always be a spot for the second player to move. This strategy will 
work for ANY symmetric starting position. How, then, is the round table a FIRST
player win? at the beginning of the game there is exactly 1 move which
preserves the symmetry of the playfield; (0,0). First player moves there and
then pretends to be the second player. 

Better Problem: (for this problem, assume the Penny Width (PW) to be the 
unit of distance) Two players are about to play this game on a round table 
of diameter N PW, for unknown N. Unfortunately, a Malicious Mathematician has 
Krazy Glued a penny to position (0,.5PW). Determine the set of real numbers N
for which this game is a first player win.


-- 
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sit down someday and make a list of all things that don't
any difference to you. when you are done, throw away the list.
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                                         -the venn buddhist