What is Triangle Peg Solitaire?
Triangle Peg Solitaire is played on 15 holes arranged in a triangle of five rows: one hole at the top, then two, three, four and five. The game starts with 14 pegs and the top corner empty.
A peg jumps over a neighbouring peg into the empty hole straight beyond it, and the jumped peg is removed, as on the cross-shaped boards. On the triangle every hole lies on three lines, the rows and the two slopes, so a peg can jump in six directions.
You win by leaving one peg. With only 13 jumps the game is short, but pegs left in the corners are easily stranded.
Rule changes
| Rule | Standard Peg Solitaire | Triangle Peg Solitaire |
|---|---|---|
| Board | Standard Peg Solitaire33 holes in a cross on a square grid. | Triangle Peg Solitaire15 holes in a triangle of five rows. |
| Jumps | Standard Peg SolitaireAlong rows and columns only: four directions. | Triangle Peg SolitaireAlong the rows and both slopes of the triangle: six directions. |
| Empty hole at the start | Standard Peg SolitaireThe centre hole, with 32 pegs on the board. | Triangle Peg SolitaireThe top corner, with 14 pegs on the board. |
| Jumps in a solution | Standard Peg Solitaire31. | Triangle Peg Solitaire13. |
| Finish in the starting hole | Standard Peg SolitaireOffered as an option: the last peg must end in the centre. | Triangle Peg SolitaireOffered as an option: the last peg must end in the top corner, where the empty hole started. |
History
The 15-hole triangle is a common form of the puzzle today, often sold as a small wooden board played with golf tees as pegs.
Because a triangular board has three lines of jumps instead of two, it behaves differently from the square boards. George I. Bell studied triangular boards of many sizes in Solving Triangular Peg Solitaire (Journal of Integer Sequences, 2008), working out from which empty holes they can be solved and where the last peg can end.