As a general hint for peg puzzles in all contexts, you need to consider the geometry of the puzzle and how it changes when you make moves. For example, the triangular puzzle has three central pegs surrounded by a row of pegs on the edge of the puzzle. You may notice that you can never jump an edge peg over another edge peg and land in the center. Therefore, if you have two central pegs and jump one over the other, you'll land on the edge and the center will be forever empty! You can only preserve those central pegs by jumping edge pegs over them and into the empty spaces in the center. This is true for peg-jumping games of all shapes and sizes, and is vital to keep in mind as you formulate your solutions.