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.
... 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.
Also, that was some beautiful math. Thanks.
posted by benito.strauss at 9:25 AM on August 15, 2014
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
posted by The Bellman at 10:11 AM 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]
posted by motty at 1:27 PM on August 15, 2014 [1 favorite]
A problem with a similar kind of solution
posted by eruonna at 3:14 PM on August 15, 2014 [1 favorite]
posted by eruonna at 3:14 PM on August 15, 2014 [1 favorite]
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posted by benito.strauss at 9:23 AM on August 15, 2014 [2 favorites]