A ug 2 00 7 SOLVING TRIANGULAR PEG SOLITAIRE
نویسنده
چکیده
We consider the one-person game of peg solitaire on a triangular board of arbitrary size. The basic game begins from a full board with one peg missing and finishes with one peg at a specified board location. We develop necessary and sufficient conditions for this game to be solvable. For all solvable problems, we give an explicit solution algorithm. On the 15-hole board, we compare three simple solution strategies. We then consider the problem of finding solutions that minimize the number of moves (where a move is one or more consecutive jumps by the same peg), and find the shortest solution to the basic game on all triangular boards with up to 55 holes (10 holes on a side).
منابع مشابه
Solving Triangular Peg Solitaire
We consider the one-person game of peg solitaire on a triangular board of arbitrary size. The basic game begins from a full board with one peg missing and finishes with one peg at a specified board location. We develop necessary and sufficient conditions for this game to be solvable. For all solvable problems, we give an explicit solution algorithm. On the 15-hole board, we compare three simple...
متن کامل2 5 Ju n 20 07 SOLVING TRIANGULAR PEG SOLITAIRE
We consider the one-person game of peg solitaire on a triangular board of arbitrary size. The basic game begins from a full board with one peg missing and finishes with one peg at a specified board location. We develop necessary and sufficient conditions for this game to be solvable. For all solvable problems, we give an explicit solution algorithm. On the 15-hole board, we compare three simple...
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The classical game of Peg Solitaire has uncertain origins, but was certainly popular by the time of LOUIS XIV, and was described by LEIBNIZ in 1710. The modern mathematical study of the game dates to the 1960s, when the solitaire cone was first described by BOARDMAN and CONWAY. Valid inequalities over this cone, known as pagoda functions, were used to show the infeasibility of various peg games...
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We consider the one-person game of peg solitaire played on a computer. Two popular board shapes are the 33-hole cross-shaped board, and the 15-hole triangular board—we use them as examples throughout. The basic game begins from a full board with one peg missing and finishes at a board position with one peg. First, we discuss ways to solve the basic game on a computer. Then we consider the probl...
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