I don't remember the hardest one, so here is one of the other questions from the perspective of the interviewer. Here is a coin game as follows. We each have three fair coins, and we flip all of them at once. After we flip them, we look at the outcomes. If we have the same number of heads out of our own coins I pay you $1 and if we have a different number you pay me $2. Do you want to play this game?