## Or, the 15-hole triangular board made easy ...

This crafty peg solitaire puzzle can be frustrating. The theory behind the game is extensive, but if you just want to solve the puzzle, this page is for you! Starting from a board with one peg missing, the goal is to jump pegs (removing the jumped peg) and finish with only one peg.

There are two ways to use this web site. You can read over the tips below, and go back and try to solve the puzzle yourself, or you can memorize a solution and amaze your friends (solutions are given on the next page).

Note the symmetry of the triangular board: there are three corner holes (red), three interior holes (green), and three holes at the midpoint of each edge (blue), plus six "other" holes (yellow).

The following rules of thumb are based on a mathematical analysis of the game and should help you solve the puzzle:

1. Avoid jumping into a corner. Of course, in some situations (such as beginning without a corner peg) this is the only jump possible.
2. Avoid any jump which starts from one of the green interior holes. Such a move is almost always a dead end (none of the solutions on the next page include this jump).
3. The easiest place to begin the game is with the missing peg (hole) at one of the blue midpoint locations. The hardest place to begin is with the missing peg at one of the green interior holes.

These rules of thumb are easy to remember: "Don't jump into a corner or out of the center".

A 2008 paper [P4] quantifies how much this rule helps a player who selects jumps at random (surely you can do better than that!).

Stop here if you want to try the puzzle again with these tips. Follow this link to play my online version of this game. If you are really stumped, this version will point out all jumps that lead to a dead end. If you look for these clues, you will lever lose!

Triangular Peg Solitaire Main Page ...