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Recreational Mathematics Magazine

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Mathematical Citation Quotient (MCQ) 2016: 0.05

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2182-1976
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Designing Peg Solitaire Puzzles

George I. Bell
Published Online: 2017-06-09 | DOI: https://doi.org/10.1515/rmm-2017-0011

Abstract

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 computed solvable symmetric board positions for four board shapes. A new idea is to search for board positions which have a unique starting jump leading to a solution. We show many challenging puzzles uncovered by this search technique. Clever solvers can take advantage of the uniqueness property to help solve these puzzles.

Keywords: Solitaire puzzles; game design

References

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  • [2] Berlekamp, E., Conway, J., Guy, R. “Purging pegs properly”, in Winning Ways for Your Mathematical Plays, 2nd ed., Vol. 4, Chap. 23: 803-841, A K Peters, 2004.Google Scholar

  • [3] Gardner, M. “Peg Solitaire”, in Knots and Borromean Rings, Rep-Tiles and Eight Queens, Cambridge Univ. Press, 2014.Google Scholar

  • [4] Bell, G. “Triangular peg solitaire unlimited”, Games and Puzzles Journal, 36, 2004. http://www.gpj.connectfree.co.uk/gpjr.htm http://arxiv.org/abs/0711.0486Google Scholar

  • [5] Bell, G. “Solving triangular peg solitaire”, Journal of Integer Sequences, 11, 2008. http://arxiv.org/abs/math/0703865Google Scholar

  • [6] Beasley, J. “On 33-hole solitaire positions with rotational symmetry”, 2012. http://www.jsbeasley.co.uk/puzzles/solitairerotations.pdfGoogle Scholar

  • [7] Bell, G. “Notes on solving and playing peg solitaire on a computer”, 2014. http://arxiv.org/abs/0903.3696Google Scholar

  • [8] Bell, G. Peg Solitaire web site, http://www.gibell.net/pegsolitaire/Google Scholar

  • [9] Bell, G. Symmetric English positions, http://www.gibell.net/pegsolitaire/Tools/Symmetric/English.htmGoogle Scholar

  • [10] Bell, G. Symmetric French positions, http://www.gibell.net/pegsolitaire/Tools/Symmetric/French.htmGoogle Scholar

  • [11] Bell, G. Symmetric 6x6 positions, http://www.gibell.net/pegsolitaire/Tools/Symmetric/SixBySix.htmGoogle Scholar

  • [12] Bell, G. Symmetric Hexagon positions, http://www.gibell.net/pegsolitaire/Tools/Hex37/Symmetric.htmGoogle Scholar

  • [13] Bell, G. Difficult English positions, http://www.gibell.net/pegsolitaire/Tools/Difficult/English0.htmGoogle Scholar

  • [14] Bell, G. Difficult French positions, http://www.gibell.net/pegsolitaire/Tools/Difficult/French0.htmGoogle Scholar

  • [15] Bell, G. Difficult Hexagon positions, http://www.gibell.net/pegsolitaire/Tools/Hex37/Difficult.htmGoogle Scholar

About the article

Published Online: 2017-06-09

Published in Print: 2017-05-24


Citation Information: Recreational Mathematics Magazine, Volume 4, Issue 7, Pages 5–19, ISSN (Online) 2182-1976, DOI: https://doi.org/10.1515/rmm-2017-0011.

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© 2017. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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