Triangular Peg Solitaire Unlimited

Abstract: Triangular peg solitaire is a well-known one-person game or puzzle. When one peg captures many pegs consecutively, this is called a sweep. We investigate whether the game can end in a dramatic fashion, with one peg sweeping all remaining pegs off the board. For triangular boards of side 6 and 8 (with 21 and 36 holes, respectively) the geometrically longest sweep can occur as the final move in a game. On larger triangular boards, we demonstrate how to construct solutions that finish with arbitrarily long sweeps. We also consider the problem of finding solutions that minimize the total number of moves (where a move is one or more consecutive jumps by the same peg).