A triangular version of Peg Solitaire with 15 holes and 14 pegs. Numbering hole 1 at the apex of the triangle and thereafter from left to right on the next lower row, etc., the following table gives possible ending holes for a single peg removed (Beeler et al. 1972, Item 76). Because of symmetry, only the first five pegs need be considered. Also because of symmetry, removing peg 2 is equivalent to removing peg 3 and flipping the board horizontally.
|remove||possible ending pegs|
|1||1, , 13|
|2||2, 6, 11, 14|
|4||, 4, 9, 15|
Beeler, M.; Gosper, R. W.; and Schroeppel, R. Item 75 in HAKMEM. Cambridge, MA: MIT
Artificial Intelligence Laboratory, Memo AIM-239, Feb. 1972.