observes a switch in parity (from even to odd), meaning that she herself is wearing a white hat which causes the change in parity! So she says “white” the correct answer. The third tallest person now knows that the parity of white hats that he should observe now an odd number having heard from the first two people. He observes 5 white hats, an odd number, meaning that there is no change in parity, thus he is able to deduce that he is wearing a black hat. This process repeats again until the shortest person successfully guesses the correct answer. Congratulations! All of you are safely released! Looks like humans are intelligent life forms after all.
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