Masks on the Staircase

100 100 performers stand on a staircase, one per step, all facing downhill, and a director places either a black or a white mask on each (any combination is possible). Each performer sees every mask below them but not their own nor any behind. Starting from the top of the staircase and moving down, each must call out \"black\" or \"white\"; a performer who names their own mask color wins a prize. Everyone hears every call. With a strategy agreed beforehand, how many prizes can the troupe guarantee?

Answer

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