Resources for NIMDate: 07/03/97 at 11:25:04 From: Bill Sanford Subject: A math game called NIM I have been told that NIM is a Chinese game involving capturing theory, but I can't find anything about it. Do you know what NIM is? Bill Date: 07/03/97 at 12:51:10 From: Doctor Rob Subject: Re: A math game called NIM Bill, The original form of NIM is as follows. 12 matches are arranged in three rows of 3, 4, and 5: | | | | | | | | | | | | Two players alternate turns. In one turn, each player can take any number of matches out of any one row. The player who takes the last match wins. It turns out that the first player has a winning strategy. (Can you find the winning first move?) The strategy has a mathematical description, but it is very much not obvious what it is. There are many variations. One is where the player who takes the last match *loses*. Others involve starting with different numbers of matches in the rows, and different numbers of rows. Still another allows the splitting of a row into two as you take some of the matches (e.g., take the middle match from the last row, leaving 2 rows of 2 matches each). Martin Gardner has written about this game in one of his books, which have titles similar to these: Gardner, Martin, _The Scientific American Book of Mathematical Puzzles and Diversions_ Gardner, Martin, _The Second Scientific American Book of Mathematical Puzzles and Diversions_ (New York: Simon and Schuster, 1961) Gardner, Martin, _New Mathematical Diversions from Scientific American_ (New York: Simon and Schuster, 1966) These are reprints of his "Mathematical Games" column from the magazine _Scientific American_ which appeared in the 1960s and 1970s. Another source would be: Berlekamp, Elwyn R.; Conway, John Horton; and Guy, Richard K., _Winning Ways, for Your Mathematical Plays_ (New York: Academic Press, 1985), 2 volumes. Probably volume 2 would include NIM. -Doctor Rob, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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