* * * * *
That darned Peg Game, Part III
Bunny and I were at the Cracker Barrel [1] playing the ever ubiquitous Peg
Game [2]. As I was struggling with the game (I am phenomienally bad at that
game [3]—so bad I have my computer do it for me [4]) 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?
[1]
http://www.crackerbarrel.com/
[2]
http://shop.crackerbarrel.com/Peg-Game/dp/B0050PMMQA?field_availability=-2&field_browse=2808085011&id=Peg+Game&ie=UTF8&refinementHistory=brandtextbin%2Csubjectbin%2Ccolor_map%2Cprice%2Csize_name&searchNodeID=2808085011&searchPage=1&searchRank=salesrank&searchSize=12
[3]
gopher://gopher.conman.org/0Phlog:2008/03/16.3
[4]
gopher://gopher.conman.org/0Phlog:2005/03/18.1
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