Many of you may be familiar with a puzzle game that consists of a 15-peg triangle and is dubbed as "The Original IQ Test". The idea behind the game is that you fill 14 of the 15 holes with pegs, and the way to play is to "jump" another peg into an empty space adjacent to the peg that is being jumped over. After the jump is completed, the peg that is jumped over is removed from the triangle. The goal of the game is to jump the pegs in such a way that in the end, there is only one peg left.
My questions are:
Is there a solution for every starting configuration i.e. no matter what hole is left unfilled in the beginning? If so, are there solutions for each hole for every $n$-peg triangle?
Is there a definitive algorithm for completing the puzzle no matter what peg is left unfilled in the beginning?
Is there only 1 unique solution for every starting configuration?
I have played around with the puzzle for a little bit, but I haven't been able to complete it with one peg left but rather two. Any help with this problem would be appreciated, thanks!
Here is a link to the picture of the board: http://i.imgur.com/NuaHuPg.jpg