PRESENTER: Dr. Ray Seyfarth

Dr. Ray Seyfarth first explained the traditional approach to solving small (e.g., seven rows with 28 peg positions) triangular peg puzzles. This traditional approach requires storing all of the state information for all possible 2ⁿ states, where n is the number of peg positions. The search technique is essentially random, with the state array storing the list of feasible future moves to make, i.e., if backtracking is used.

For large puzzles, however, Dr. Seyfarth abandons the traditional random search with backtracking, in favor of planned, nonrandom moves, that eliminate pegs starting from the bottom row all the way up to row seven. Dr. Seyfarth also provided a list of heuristics for solving large peg puzzles.

The triangle peg puzzle is a puzzle game played on a triangular board, so there are only three types of valid bidirectional moves: (1)left sideways movements, (2) right sideways movements, and (3)lateral movements. Valid movements occur when three contiguous peg positions filled with pegs are all on the same horizontal row, or all on the same left or right diagonal and have one of the two following patterns: (1)peg present, peg present, peg absent, or (2)peg absent, peg present, peg present. Initially, one peg position known as the starting peg position is left empty.

Dr. Ray Seyfartht explained the traditional approach to solving small (e.g., seven rows with 28 peg positions) triangular peg puzzles. This traditional approach requires storing all of the state information for all possible 2ⁿ states, where n is the number of peg positions, so that infeasible states will not be tried again. The search technique is essentially random, with the state array storing the list of feasible future moves to make, i.e., if backtracking is used.

For large puzzles, however, Dr. Seyfarth abandons the traditional random search with backtracking, in favor of planned, nonrandom moves, that eliminate pegs starting from the bottom row all the way up to row seven. Once all pegs have been removed from rows n through n-7, then the traditional peg puzzle solution for a seven row peg puzzle can be used. This results in a peg puzzle solution that is O(n³) rather than O(2ⁿ).

Dr. Seyfarth also provided a list of heuristics for solving large peg puzzles. Some of these heuristics are the following ones:

1. Use the strategy of eliminating pegs from bottom rows up to row seven, then use the regular approach.
2. Use the strategy of picking the best left or right diagonal move.
3. Use the general principles of:

(b)avoiding jumps that place pegs in the corners of the board.

Dr. Ray Seyfarth first explained the traditional approach to solving small triangular peg puzzles. This traditional approach requires storing all of the state information for all possible 2ⁿ states, where n is the number of peg positions. The search technique is essentially random, with the state array storing the list of feasible future moves to make, i.e., if backtracking is used.

For large puzzles, however, Dr. Seyfarth abandons the traditional random search with backtracking, in favor of planned, nonrandom moves, that eliminate pegs starting from the bottom row all the way up to row seven or above. Dr. Seyfarth also provided a list of heuristics for solving large peg puzzles. The use of these heuristics results in a peg puzzle solution that is O(n³) rather than O(2ⁿ).

Dr. Seyfarth also provided a list of heuristics for solving large peg puzzles. The list of heuristics includes the use of the strategy of picking the best left or right diagonal move and the use of the general principle of favoring jumps that are in the middle of the board over those at the edges of the board.

I believe that Dr. Seyfarth is correct in his approach to solving large peg puzzles. I believe that it is correct to abandon the traditional random search with backtracking, in favor of planned, nonrandom moves, that eliminate pegs starting from the bottom row all the way up to row seven. However, I do not see why the traditional approach has to be used at all, since a planned, nonrandom, operations research heuristic algorithm could solve an entire peg puzzle, and not just the n through n-7 rows of a peg puzzle.