I think there's a better way to think about the Jack-Anne-George problem, which generalizes more readily. You've got a chain with "married" at one end and "unmarried" at the other: so of course at some point along it there has to be a transition from the former to the latter, QED.
That is a very tidy analysis.
Easier than enumerate and evaluate, but much less general.
http://www.scientificamerican.com/article/rational-and-irrational-thought-the-thinking-that-iq-tests-miss/