Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP
Posting-Version: version B 2.10.3 4.3bsd-beta 6/6/85; site sdcrdcf.UUCP
Path: utzoo!linus!decvax!ittatc!dcdwest!sdcsvax!sdcrdcf!markb
From: markb@sdcrdcf.UUCP (Mark Biggar)
Newsgroups: net.puzzle
Subject: Re: pennies puzzle (SPOILER)
Message-ID: <2637@sdcrdcf.UUCP>
Date: Thu, 20-Feb-86 16:40:51 EST
Article-I.D.: sdcrdcf.2637
Posted: Thu Feb 20 16:40:51 1986
Date-Received: Mon, 24-Feb-86 07:32:09 EST
References: <953@houxa.UUCP>
Reply-To: markb@sdcrdcf.UUCP (Mark Biggar)
Organization: System Development Corporation R&D, Santa Monica
Lines: 29

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.

Necessary Assumption: pennies must not overlap, but may touch.

Winning strategy for the first player is as follows:

1.  Make your first move to the exact center of the table.

2.  On each following move place your penny exactly on the other side of
        of the center penny form your opponents move.  If the
        other player places a penny 3 inches north of the center
        penny you place one 3 inches south of it.  As there will
        always be a place for you to put a penny you will always
        place the last one.

A much more difficult problem is a winning stratagy if the last person
to be albe to place a penny loses.

Mark Biggar
{allegra,burdvax,cbosgd,hplabs,ihnp4,akgua,sdcsvax}!sdcrdcf!markb