@StAnn:
Sorry I didn't give you credit where it was due. I didn't have time to go back and see who had said 13/27 before getting to work this morning. That odd figure stood out, I just had to figure out where it came from and if it was right or wrong. As usual, you were right!
@Bohm:
Thank you for the fun thread! I didn't read your response until this evening.
@everybody:
Solving this class of problem requires more than one tool. The first tool is the basic probability part, identifying the number of permuations (there are 196: (two genders x seven days of the week) ^ two children = 14 ^ 2 = 196). The second tool is deductive reasoning, determining which of the permutations the observer's statements have excluded. You need to use both tools to make sense of "Monty Hall Problems": it isn't just about finding the over-all distribution, it's identifying which particular outcomes are consistent with observations based on "inside knowledge" of the permutation that turned up in this particular instance. It looks like a pure probability problem, but the reporter with inside information changes the game.