During my analysis, i used a simple Cartesian mapping convention where x represented the row of the location and y represented the column. The symmetry can be seen by assigning a name to each location on the board then calculating each positions' ability to jump an adjacent piece and its' ability to be jumped by an adjacent piece.

Each of the non-recursive techniques can be obtained by observation of the board’s symmetry. Basically, there is an empty hole for the peg completing the jump to land in.Ī truly non recursive solution method for all potential board configurations does not exist however there are some very useful techniques that can significantly increase the chances that a successful solution can be found.

There is an empty hole immediately adjacent to the peg being jumped and it is in line with the peg completing the jump.

The peg to be jumped is diagonally across from the peg completing the jump (+ or - one row and + or - one column).

The peg to be jumped is horizontally across from to the peg completing the jump.

The peg that will be performing the jump is immediately adjacent to the peg that will be jumped.

Jumps are legal if the following conditions are met: Similar to checkers when a peg is jumped, it is removed from the game board. The game is played by jumping one peg over another and into an empty hole. The hole that remains empty is arbitrary however my investigation was done with the empty hole always at one of the three corners of the game board (row 1 hole 1). The board is initially setup with 14 holes occupied by pegs or golf tees.

For example row 1 contains 1 hole row 2 contains 2 holes etc. Each row contains the same number of holes as its row number for a total of 15 holes. For the purpose of this project, I chose the triangular 5 row variation. Peg Solitaire is a game that consists of a geometric game board containing holes. 2.2.3 Analysis of the Complete Recursive Solution.

2 sided peg solitaire