Solution:Alice reasons that if her hat were black then Barbara would know at once that her hat is white, because that would be the only way to explain Charlottes raised hand. But Barbara doesnt know the color of her hat; so she must be seeing a white hat on Alices head.
This is rather different from what happens in Whats That on My Head? because in the game you dont rely on what the other players are thinking. But maybe in a rare instance you could take into account the reasoning of other players.
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