Journal of Integer Sequences, Vol. 11 (2008), Article 08.4.8

Solving Triangular Peg Solitaire

George I. Bell
Tech-X Corporation
5621 Arapahoe Ave, Suite A
Boulder, CO 80303


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).

Full version:  pdf,    dvi,    ps,    latex    

(Concerned with sequences A120422 A127500 A130515 and A130516.)

Received August 1 2008; revised version received November 12 2008. Published in Journal of Integer Sequences, November 16 2008.

Return to Journal of Integer Sequences home page