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From: dim@whuxlm.UUCP (McCooey David I)
Newsgroups: net.puzzle
Subject: Re: pennies puzzle (SPOILER)
Message-ID: <905@whuxlm.UUCP>
Date: Wed, 19-Feb-86 12:49:48 EST
Article-I.D.: whuxlm.905
Posted: Wed Feb 19 12:49:48 1986
Date-Received: Thu, 20-Feb-86 07:47:28 EST
References: <953@houxa.UUCP> <904@whuxlm.UUCP>
Organization: AT&T Bell Laboratories, Whippany
Lines: 32

> > 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.
> > 
> The second player can always win if he uses the following strategy:
> 
> 	Considering the center of the table as the "origin", always
> 	place his penny at a spot reflected through the origin from
> 	where his opponent just placed his last penny.
> 
> Using this strategy, the second player will always have a spot to place his
> penny because he is simply mirroring the actions of the first player.
> 
> 					Dave McCooey
> 					AT&T Bell Labs, Whippany
> 					ihnp4!whuxlm!dim

Actually, the above strategy has a flaw:  The first player starts off by
placing his penny on the origin.  Therefore, it is the FIRST player that
has a winning strategy.  He just uses the strategy given above AFTER his
first move, which is at the origin.

					Dave McCooey
					AT&T Bell Labs, Whippany
					ihnp4!whuxlm!dim