منابع مشابه
Reversible 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 ...
متن کاملPeg solitaire on the windmill and the double star graphs
In a recent work by Beeler and Hoilman, the game of peg solitaire is generalized to arbitrary boards. These boards are treated as graphs in the combinatorial sense. In this paper, we extend this study by considering the windmill and the double star. Simple necessary and sufficient conditions are given for the solvability of each graph. We also discuss an open problem concerning the range of val...
متن کاملOne-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...
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ژورنال
عنوان ژورنال: Involve, a Journal of Mathematics
سال: 2018
ISSN: 1944-4184,1944-4176
DOI: 10.2140/involve.2018.11.53