I played Bulgarian Solitaire with math teachers at Lawrence High on January 11, 2011. What's Bulgarian Solitaire? See http://en.wikipedia.org/wiki/Bulgarian_solitaire , although we used coins instead of cards.
Three follow-up items:
- We didn't get a chance to discuss "Garden of Eden" configurations, but I wanted to point out how this is such a great name. A Garden of Eden position is one that can't be reached from any other configuration in the game. The name does such a good job of capturing the idea behind it!
- Unlike positions that create one-cycles, which we discussed and seem to be rare, there seem to be lots of Gardens of Eden as you increase the number of coins/cards in the game. For example (2,2,2,2,.....) where there are at least four 2's is Garden of Eden. Do you see why?
- Technology. You get some interesting macroscopic information about what happens when you change the number of coins by generating state graphs like the one you see above for 10 coins.
I've prepared a Mathematica Notebook that has more images. They can be viewed using Mathematica or the free Mathematica Player application.