Oooh! I feel like I should have gotten that! (Well, not really, but there was at least a chance I could have gotten that.)
Trivia: I have actually had game 11982 given to me. And that broke my attempt to get to 200 wins in a row. I was a little mad about that, but given the number of times I've broken the streak on my own, I guess it was nothing to get upset about.
so I didn't comment. But, I took a few shots at it but my usual strategy was a complete bust very early. I think the problem comes down to formulating the possible moves of the game as a graph, and proving that it either is or isn't connected. I haven't thought hard enough about how to do that formulation, though.