  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).

Combinatorics;Discrete Mathematics