Peg game
So... I was curious one evening comming back from Cracker Barrel...

How many ways were there to win at that infamous peg game?

So, being the computer guy I am, I wrote PegGame.java to figure it out. (n pegs left means there's no possible moves)

Possible boards: 13935
Total ways to play: 7335390

1 peg left (win): 438984
2 pegs left: 1776648
3 pegs left: 3302124
4 pegs left: 1605348
5 pegs left: 197670
6 pegs left: 11160
7 pegs left: 3438
8 pegs left: 12
9 pegs left: 0
10 pegs left: 6
11 pegs left: 0
13 pegs left: 0
12 pegs left: 0
14 pegs left: 0



And here is the entire game tree in a very simple graphical format. (It might take a couple seconds to generate.) Navigate by clicking on the boards.

Source: PegGraphics.java, PegGameApplet.java.