Designing Peg Solitaire Puzzles

Open access

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.

[1] Beasley, J. The Ins and Outs of Peg Solitaire, Oxford Univ. Press, 1992.

[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.

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

[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/0711.0486

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

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

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

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

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

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

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

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

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

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

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

Journal Information

Target Group

researchers in the fields of games and puzzles, problems, mathmagic, mathematics and arts, math and fun with algorithms

Metrics

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 142 142 18
PDF Downloads 47 47 12