judith@proper.UUCP (Judith Abrahms) (09/06/85)
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 ------------------------------------------------------------------------------ "The sames should stay with the sames, and the differents should stay with the differents." -- A. Bunker ------------------------------------------------------------------------------
putnam@steinmetz.UUCP (jefu) (09/13/85)
A delightful book on Nim and other games is "Winning Ways for
Your Mathematical Plays" by Berlekamp ("Algebraic Coding Theory"),
Conway ("On Numbers and Games", the game of life), and Guy (American
Mathematical Monthly). Should the titles mentioned sound imposing,
they are, but the book is easy to follow, even for the mathematical
novice (well, mostly), well written, and even wonderfully illustrated.
Dont miss it!
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