[zem]

i did it by thinking "let bob pick a strategy, and let alice pick her answer by knowing what bob is going to do. if bob always guesses his own coin, then when alice sees H she knows that either bob has H too and will therefore win for both of them, or bob has T and will therefore lose, but the only way to lose is if bob has T so if alice guesses T then they have all their bases covered". of course there is a simpler way to get the answer, as other posters have noted.