The Boston Diaries

The ongoing saga of a programmer who doesn't live in Boston, nor does he even like Boston, but yet named his weblog/journal “The Boston Diaries.”

Go figure.

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?

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