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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…

Combinatorics · Mathematics 2009-01-17 George I. Bell

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…

Combinatorics · Mathematics 2007-11-29 George I. Bell

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 triangle board---we use them as examples throughout. The basic game begins from a full board…

Combinatorics · Mathematics 2014-11-07 George I. Bell

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…

Combinatorics · Mathematics 2007-05-23 George I. Bell

Peg solitaire is an old puzzle with a 300 year history. We consider two ways a computer can be utilized to find interesting peg solitaire puzzles. It is common for a peg solitaire puzzle to begin from a symmetric board position, we have…

History and Overview · Mathematics 2017-09-12 George I. Bell

Peg solitaire is classically a one-player game played on a grid board containing pegs. The goal of the game is to have a single peg remaining on the board by sequentially jumping with a peg over an adjacent peg onto an empty cell while…

Combinatorics · Mathematics 2022-12-07 Valentino Vito

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 reducing any…

Combinatorics · Mathematics 2007-05-23 Cristopher Moore , David Eppstein

Peg solitaire is a game generalized to connected graphs by Beeler and Hoilman. In the game pegs are placed on all but one vertex. If $xyz$ form a 3-vertex path and $x$ and $y$ each have a peg but $z$ does not, then we can remove the pegs at…

Combinatorics · Mathematics 2014-03-03 Jennifer Wise , Sarah Loeb

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 reducing any…

Combinatorics · Mathematics 2007-05-23 Cristopher Moore , David Eppstein

Despite its long history, the classical game of peg solitaire continues to attract the attention of the scientific community. In this paper, we consider two problems with an algorithmic flavour which are related with this game, namely…

Discrete Mathematics · Computer Science 2016-05-16 Luciano Gualà , Stefano Leucci , Emanuele Natale , Roberto Tauraso

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 $G$. If $xyz$ forms a path in $G$ and there are pegs on vertices $x$ and $y$ but not…

Combinatorics · Mathematics 2015-05-13 John Engbers , Christopher Stocker

"Solitaire Chess" is a logic puzzle published by Thinkfun, that can be seen as a single person version of traditional chess. Given a chess board with some chess pieces of the same color placed on it, the task is to capture all pieces but…

Computational Complexity · Computer Science 2015-01-27 Jens Maßberg

Tetravex is a widely played one person computer game in which you are given $n^2$ unit tiles, each edge of which is labelled with a number. The objective is to place each tile within a $n$ by $n$ square such that all neighbouring edges are…

Computational Complexity · Computer Science 2012-04-18 Yasuhiko Takenaga , Toby Walsh

In the game of pegging, each vertex of a graph is considered a hole into which a peg can be placed. A pegging move is performed by jumping one peg over another peg, and then removing the peg that has been jumped over from the graph. We…

Combinatorics · Mathematics 2011-03-03 Ariel Levavi

We consider the problem of determining the minimum number of moves needed to solve a certain one-dimensional peg puzzle. Let N be a positive integer. The puzzle apparatus consists of a block with a single row of 2N+1 equally spaced holes…

Combinatorics · Mathematics 2007-05-23 David M. Bradley , Hugh Thomas

Clobber is a new two-player board game. In this paper, we introduce the one-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…

Discrete Mathematics · Computer Science 2007-05-23 Erik D. Demaine , Martin L. Demaine , Rudolf Fleischer

We analyze the computational complexity of several new variants of edge-matching puzzles. First we analyze inequality (instead of equality) constraints between adjacent tiles, proving the problem NP-complete for strict inequalities but…

We analyze Solo Chess puzzles, where the input is an $n \times n$ board containing some standard Chess pieces of the same color, and the goal is to make a sequence of capture moves to reduce down to a single piece. Prior work analyzes this…

Computational Complexity · Computer Science 2023-02-06 Josh Brunner , Lily Chung , Michael Coulombe , Erik D. Demaine , Timothy Gomez , Jayson Lynch

The solitaire of independence is a groupoid action resembling the classical 15-puzzle, which gives information about independent sets of coordinates in a totally extremally permutive subshift. We study the solitaire with the triangle shape,…

Combinatorics · Mathematics 2022-06-10 Ville Salo , Juliette Schabanel

In this paper, we study a reversible process (more precisely, a groupoid/group action) resembling the classical 15-puzzle, where the legal moves are to ``move the unique hole inside a translate of a shape $S$''. Such a process can be…

Combinatorics · Mathematics 2024-10-01 Ville Salo , Juliette Schabanel
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