  We investigate the game of peg solitaire on different board shapes, and find
those of diamond or rhombus shape have interesting properties. When one peg
captures many pegs consecutively, this is called a sweep. Rhombus boards of
side 6 have the property that no matter which peg is missing at the start, the
game can be solved to one peg using a maximal sweep of length 16. We show how
to construct a solution on a rhombus board of side 6i, where the final move is
a maximal sweep of length r, where r=(9i-1)(3i-1) is a "rhombic matchstick
number".
