It's just a jump to the ... well, in any legal direction really
August 15, 2014 8:49 AM   Subscribe

The Peg Solitaire Army is a problem spun off from a classic recreation, and yet another example of the golden ratio turning up where you least expect it. If you want to look at the game more deeply, George Bell's solitaire pages are the ne plus ultra: There's more about the solitaire army (and variants), ...

... peg solitaire on all kinds of square-grid boards and triangular peg solitaire.

If you want to read more about why the traditional cross-shaped, 33-hole board is special, A Fresh Look at Peg Solitaire [PDF] explains its unique properties.

If you just want to solve puzzles, there are both square and triangular games to play. The puzzles with diagonal moves allowed are an especially fun variant if you're a jaded veteran of the usual game.

And if you want neat connection to formal languages, this short paper gives a grammar for recognizing solvable positions in 1-dimensional peg solitaire.
posted by Wolfdog (6 comments total) 14 users marked this as a favorite
Of course it's John Horton Conway. If you want to watch 8 minutes of a man taking a silly little math problem and turning it into a complete theory with an accompanying periodic table of digit blocks that answer any and all questions about the silly little math problem, go here.
posted by benito.strauss at 9:23 AM on August 15, 2014 [2 favorites]

Also, that was some beautiful math. Thanks.
posted by benito.strauss at 9:25 AM on August 15, 2014

I watched that video and I thought, "oh wait, this is going to be like Life, isn't it?" and then I thought "Oh yeah. Duh."
posted by The Bellman at 10:11 AM on August 15, 2014

Too much for this eg-no-ra-moose.
posted by scruss at 12:09 PM on August 15, 2014

After reading through why no peg can reach row 5, it's worth reading Simon Tatham's proof, linked from one of the OP's pages, that, with one small tweak, it can be done after all.
posted by motty at 1:27 PM on August 15, 2014 [1 favorite]

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