Even though trying to solve the peg puzzle seems impossible to most people, there are more than 400,000 solutions to it; the missing peg can be in any of the 15 holes. That statistic is insignificant, though, when you are frustrated trying to get rid of that next-to-the-last peg.
Arrange the board so the empty hole is in the bottom right corner
Setting up your board the way you want it is the most important step of the entire process. You may not remember every outlined step while you are sitting at the table, but you can remember how to set up the board.
Jump the first peg
The rules are that in each move one peg must jump over another and then the jumped peg is removed. Keep doing that until there is only one peg left. To identify the pegs to jump, number each hole starting with the top of the triangle and starting each new row on the left side. The peg jumping order then starts with 13 over 14.
Jump and remove remaining pegs
The following steps will then remove the rest of the pegs: 6 over 9, 15 over 10, 12 over 13, 4 over 8, 11 over 7. At this point, you will have a small triangle of 6 at the top of the board and two pegs in holes 13 and 14. Continue the jumping in this order: 3 over 6, 2 over 4, 13 over 14, 15 over 10, 6 over 5 and 7 over 4. This leaves just two pegs in holes 1 and 2. Jump 1 over 2 and you have only one peg left in hole 4.