'One-Dimensional Peg Solitaire, and Duotaire.' Working To Automata Theory, Languages, and Computation, 2nd ed. R. J. Nowakowski.) Cambridge, England: Cambridge University Press, 1998. MSRI Workshop on Combinatorial Games, July, 1994 (Ed. 'Unsolved Problems in Combinatorial Games.' In Games Cambridge, MA: MIT Artificial Intelligence Laboratory, Memo AIM-239, Unexpected Hanging and Other Mathematical Diversions. 'A Programming and Problem Solving Seminar.' Stanford University Technical Final solution, our captain comes back up to the top after they've cleared the upper deck. Ways for Your Mathematical Plays, Vol. 2: Games in Particular. Now, you're starting to see where that solution is. Oxford, England: Oxford University Press,ġ992. compute the area between y=|x| and y=x^2-6.Bell gives necessary and sufficient conditionsįor this problem to be solvable and a simple solution algorithm. To removing peg 3 and flipping the board horizontally. Also because of symmetry, removing peg 2 is equivalent Because of symmetry, only theįirst five pegs need be considered. Numbering hole 1 at the apex of the triangle and thereafterįrom left to right on the next lower row, etc., the following table gives possibleĮnding holes for a single peg removed (Beeler 1972). There is also triangular variant with 15 holes (where 15 is the 5th triangular number )Īnd 14 pegs (Beeler 1972). Strategies and symmetriesĪre discussed by Gosper et al. All holes but the middle one are initially filled with pegs. One of the most common configurations is a cross-shaped board with 33 holes. The goal is to remove all pegs but one by jumping pegs from one side of an occupied peg hole to an empty space, removing the peg which was jumped over. A game played on a board of a given shape consisting of a number of holes of which all but one are initially filled with pegs.

Triangle peg solitaire solution