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 Subj:.....Fore and Aft (S592)           From the book             "Mathematical Puzzles of Sam Loyd"              Edited by Martin Gardner              From: Dover Publications in 1959 Exchange the black and white pegs in the fewest number of moves.   I take occasion to call attention to the origin of a pretty puzzle game, or species of solitaire, which became quite popular in Europe.  It was an English invention, in that it was originated by an English sailor who spent forty years of his life at Sailor's Snug Harbor, on Staten Island, and whose proud boast was that he had sailed under Captain Randall, the founder of the institution. The old sailor used to pick up quite a little bit of extra "baccy silver," as he termed it, by selling the puzzles to visitors as fast as he could whittle them out with a jack- knife.  The game was brought out in London and enjoyed quite a run under the name English Sixteen Puzzle, but was never marketed on this side of the pond. The object of the puzzle is to transpose the positions of the black and white pegs in the fewest number of moves.  A peg may be moved from one square to an adjacent vacant square, or it may be jumped over an adjacent peg (of either color) provided it lands on a vacant square.  Only moves along rows (like a rook in chess) are permitted; no diagonal moves as in checkers. According to an eye witness, the old sailor was very proud of his expertness, and used to give purchasers a rule to perform the feat in the fewest number of plays.  He was mistaken, however, in his rule, or it must be classed along with the lost arts.  Perhaps the world has advanced since his time, for the methods given in English puzzle books, as well as mathematical works, to be the shortest, are defective and may be shortened by several moves.     ¤»¥«¤»§«¤»¥«¤»§«¤»¥«¤»§«¤»¥«¤»§«¤»¥«¤»§«¤                    THE SOLUTION   [Loyd does not give his solution to this.  Most puzzle books, he says, present a solution in 52 moves, whereas the puzzle can actually be solved in 47.  H.E.Dudeney, the British puzzle expert, went Loyd one better by reducing the number to 46. For Dudeney's beautifully summetric solution, see W. Rouse Ball's Mathematical Recreations and Essays, current edition, p. 125. - M.G.]
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