How to Play by Yourself
Sometime between dragging myself into my bed after the calculus exam and related activities last night and dragging myself back out of it in time to teach this morning, an article claiming to solve triangular peg solitaire went up on the arXiv. I’ve obviously not had time to read it, so I don’t know how good it is, but the subject matter at least should be pretty generally accessible.

Hi, I am the author of this article. The article describes the algorithm which is used in the following web solver:
http://www.geocities.com/gibell.geo/pegsolitaire/Tools/Triangular/Triang.htm
However the web solver will not allow you to select the position of the final peg, but the second algorithm described in the paper does this as well.