منابع مشابه
One-Dimensional Peg Solitaire
We solve the problem of one-dimensional peg solitaire. In particular, we show that the set of configurations that can be reduced to a single peg forms a regular language, and that a linear-time algorithm exists for playing the game.
متن کاملTriangular Peg Solitaire Unlimited
Triangular peg solitaire is a well-known one-person game or puzzle. When one peg captures many pegs consecutively, this is called a sweep. We investigate whether the game can end in a dramatic fashion, with one peg sweeping all remaining pegs off the board. For triangular boards of side 6 and 8 (with 21 and 36 holes, respectively) the geometrically longest sweep can occur as the final move in a...
متن کاملSolving 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 کاملDiagonal Peg Solitaire
We study the classical game of peg solitaire when diagonal jumps are allowed. We prove that on many boards, one can begin from a full board with one peg missing, and finish with one peg anywhere on the board. We then consider the problem of finding solutions that minimize the number of moves (where a move is one or more jumps by the same peg), and find the shortest solution to the “central game...
متن کاملReversible peg solitaire on graphs
The game of peg solitaire on graphs was introduced by Beeler and Hoilman in 2011. In this game, pegs are initially placed on all but one vertex of a graph GG. If xyz forms a path in GG and there are pegs on vertices x and y but not z, then a jump places a peg on z and removes the pegs from x and y. A graph is called solvable if, for some configuration of pegs occupying all but one vertex, some ...
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ژورنال
عنوان ژورنال: INFORMS Transactions on Education
سال: 2002
ISSN: 1532-0545,1532-0545
DOI: 10.1287/ited.2.3.99