## Monday, June 09, 2014

### That darned Peg Game, Part III

Bunny and I were at the Cracker Barrel playing the ever
ubiquitous Peg
Game. As I was struggling with the game (I am *phenomienally*
bad at that game—so bad I have my computer do it for me) when
Bunny asked, “What's the maximum number of pegs you can leave on the
board?”

That's an interesting question, and I was curious if there is any way to
do *worse* than ten pegs left.

Well, I forced my computer to play a bazillion times and the results are
interesting: ten pegs are the *most* pegs you can have left on the
board. What's more interesting is that discounting rotations and
reflections, there is only *one* way to leave ten pegs on the board
(six if you want to count reflections, rotations and reflected rotations as
distinct).

Even eight pegs is pretty darned tough as well, with only two solutions (or twelve if you include rotations, reflections and rotated reflections).

So, if leaving one means you are a genius (and there are several thousand ways to leave just one peg), what does it mean to leave ten?