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From: judith@proper.UUCP (Judith Abrahms)
Newsgroups: net.math,net.puzzle
Subject: Nim Game in Marienbad
Message-ID: <280@proper.UUCP>
Date: Fri, 6-Sep-85 07:01:35 EDT
Article-I.D.: proper.280
Posted: Fri Sep  6 07:01:35 1985
Date-Received: Mon, 9-Sep-85 03:22:05 EDT
Reply-To: judith@proper.UUCP (judith)
Organization: Proper UNIX, Oakland CA
Lines: 53
Xref: watmath net.math:2244 net.puzzle:1003


   I majored in math a long time ago.  The grad students I knew played various
games on the blackboard in the rec room... the game of Nim ceased to be played
when someone pointed out that it was completely determinate.  In case Nim is
no longer as popular as it used to be, it went like this:

   Matches (or chalk marks) were set up in rows of 3, like this:

                | | |
		| | |
		| | |
		| | |

   ... etc.  I believe there was no limit on the no. of rows allowed.  There
were two players.  A move consisted of taking 1, 2, or 3 counters from JUST
ONE ROW.  Then the next player took 1, 2, or 3 counters from that row or from
another.

   Recently I saw the film Last Year at Marienbad, which was a favorite when I
was in college, and I remembered that the match game played repeatedly in the
film was pointed out to me as a special case of Nim, but one which could be won
in exactly the same way.  In "Marienbad," the matches were arranged:

	       | | | | | | |
		 | | | | |
                   | | |
		     |

and the rules were the same.  Each player could take any or all of the matches
from one row only on each turn.  Oh, yes -- the loser was the player who was
left the last match to pick up.

   I remember hearing that the algorithm the first player would use to win 
involved powers of 2 or multiples of 4, or arithmetic mod 4.  You were supposed
to make your choice of matches so that the last draw (by the other player) plus
your draw added up to ... SOMETHING.  I can't remember.  Can anyone tell me the
rule?

   BTW I also remember that the makers of Last Year at M. didn't know the
trick.  The same man always won, but the math majors in the audience would
shriek with laughter, because the moves (up to the last few, which were pretty
obvious) were completely random, and either of them could have won any of the
games.

   Please send mail.

Thanks,
Judith Abrahms
{ucbvax,ihnp4}!dual!proper!judith
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