منابع مشابه
Solitaire Clobber
Clobber is a new two-player board game. In this paper, we introduce the 1-player variant Solitaire Clobber where the goal is to remove as many stones as possible from the board by alternating white and black moves. We show that a checkerboard configuration on a single row (or single column) can be reduced to about n/4 stones. For boards with at least two rows and columns, we show that a checker...
متن کاملDiamond Solitaire
We investigate the game of peg solitaire on different board shapes, and find those of diamond or rhombus shape have interesting properties. When one peg captures many pegs consecutively , this is called a sweep. Rhombus boards of side 6 have the property that no matter which peg is missing at the start, the game can be solved to one peg using a maximal sweep of length 16. We show how to constru...
متن کاملSolitaire Lattices
One of the classical problems concerning the peg solitaire game is the feasibility issue. Tools used to show the infeasibility of various peg games include valid inequalities, known as pagoda-functions, and the so-called rule-of-three. Here we introduce and study another necessary condition: the solitaire lattice criterion. While the lattice criterion is shown to be equivalent to the rule-ofthr...
متن کاملSolitaire Games ∗
The model-checking games associated with fixed-point logics are parity games, and it is currently not known whether the strategy problem for parity games can be solved in polynomial time. We study Solitaire-LFP, a fragment of least fixedpoint logic, whose evaluation games are nested soltaire games. This means that on each strongly connected component of the game, only one player can make nontri...
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.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1992
ISSN: 0097-3165
DOI: 10.1016/0097-3165(92)90037-u