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Wythof's Nim
12-31-2019, 03:58 PM
Post: #1
Wythof's Nim
An interesting reference to the HP-67/97 programmables in PENROSE TILES to Trapdoor Ciphers ... and the return of Dr. Matrix, © 1997 by the Mathematical Association of America, chapter 8 (pgs. 103-104)

"Wythof's Nim
 An analysis of a simple two-person game can lead into fascinating corners of number theory. We begin with a charming, little known game played on a chessboard with a single queen. Before we are through, we shall have examined a remarkable pair of number sequences that are intimately connected with the golden ratio and generalized Fibonacci sequences.
 The game, which has no traditional name, was invented about 1960 by Rufus P. Isaacs, a mathematician at Johns Hopkins University. It is described briefly (without reference to chess) in Chapter 6 of the 1962 English translation of The Theory of Graphs and Its Applications, a book in French by Claude Berge. (We met Berge in the previous chapter as a member of the Oulipo.) Let's call the game "Corner the Lady."
 Player A puts the queen on any cell in the top row or in the column farthest to the right of the board; the cells appear in gray in Figure 48. The queen moves in the usual way but only west, south or southwest. Player B moves first, then the players alternate moves. The player who gets the queen to the starred cell at the lower left corner is the winner.
 No draw is possible, so that A or B is sure to win if both sides play rationally. It is easy to program an HP-97 printing calculator or the HP-67 pocket calculator to play a perfect game. Indeed, a magnetic card supplied with Hewlett-Packard's book HP-67/HP-97 Games Pac I provides just such a program."

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