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Solving Triangular Peg Solitaire
TL;DR: This work considers the one-person game of peg solitaire on a triangular board of arbitrary size, and gives an explicit solution algorithm for all solvable problems.
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Abstract: 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 also 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).
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Citations
Peg solitaire on graphs
Robert A. Beeler,D. Paul Hoilman +1 more
TL;DR: A generalization of the traditional peg solitaire to arbitrary boards is considered and it is shown that the cartesian product of two solvable graphs is likewise solvable.
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Peg solitaire on the windmill and the double star graphs.
Robert A. Beeler,D. Paul Hoilman +1 more
- 01 Jan 2012
TL;DR: This paper extends the study of the game of peg solitaire to arbitrary boards by considering the windmill and the double star, and gives simple necessary and sufficient conditions for the solvability of each graph.
Peg solitaire on trees with diameter four
Clayton A Walvoort
- 01 Jan 2013
TL;DR: In this paper, the authors give necessary and sufficient conditions for the solvability of all trees with diameter four and the maximum number of pegs that can be left on such a graph under the restriction that we jump whenever possible.
Extremal Results for Peg Solitaire on Graphs
Aaron D. Gray
- 01 Jan 2013
TL;DR: Extremal Results for Peg Solitaire on Graphs by as discussed by the authors showed that peg solitaire is a popular solver for graph-based games on graph-graphs, including graph solvers.
References
•Journal Article
The On-Line Encyclopedia of Integer Sequences.
TL;DR: The On-Line Encyclopedia of Integer Sequences (OEIS) as mentioned in this paper is a database of 13,000 number sequences and is freely available on the Web (http://www.att.com/~njas/sequences/) and is widely used.
4.7K
•Posted Content
The On-Line Encyclopedia of Integer Sequences
TL;DR: The On-Line Encyclopedia of Integer Sequences (OEIS) as discussed by the authors provides a history of the OEIS and discusses recent sequences involving interesting unsolved problems and in many cases spectacular illustrations, such as Peaceable Queens, circles in the plane, the earliest cube-free binary sequence, the EKG and Yellowstone permutations, other lexicographically earliest sequences, iteration of number-theoretic functions, home primes and power trains, a memorable prime, a missing prime, Post's tag system, and coordination sequences.
Breadth-first heuristic search
Rong Zhou,Eric A. Hansen +1 more
TL;DR: Optimal and approximate breadth-first heuristic search algorithms that use divide-and-conquer solution reconstruction and outperform other optimal and approximate heuristicsearch algorithms in solving domain-independent planning problems are described.
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