Most of us have encountered triangular peg puzzles in restaurants, which serve as an interesting diversion while waiting for food. The standard puzzle is a triangular shaped board with 5 rows of holes. Initially pegs are placed in 14 of the 15 holes on the board. The goal is to jump and remove pegs until exactly one peg remains. This tends to be fairly difficult for inexperienced solvers.

The logical extension of the 5 row puzzle is to triangular puzzles with more rows. It is easy to solve 5 and 6 row puzzles using backtracking on a computer. However puzzles with 7 or more rows are not practical for simple backtracking. The basic problem is that simple backtracking fails to record the unsolvability of puzzle states which are encountered many times during an attempt at solution.

By recording the solvability/unsolvability of puzzle states for the 7 row puzzle, it is possible to determine all solvable starting positions and to rapidly determine a solving sequence of jumps from any solvable starting position. Surprisingly to the author, there are 10 unsolvable starting positions in the 7 row puzzle and more unsolvable positions for many other sizes.

By developing a collection of heuristics the author has developed a computer program which appears successful at solving all solvable puzzles with 7 or more rows. This program has been tested on a large number of puzzles, culminating in the solution of one puzzle with 2000 rows.