An evil wizard has captured 15 dwarves of rare mathematical genius. He informs them that, the following day, he will make them stand in a circle and then from behind will place a hat, randomly either black or white, on each of their heads. He will then go to the dwarves in turn and ask each to state the colour of his hat. While each dwarf can see the colour of the others’ hats, he can see nothing of his own. If a dwarf answers correctly he can go free, otherwise he will be incarcerated for life. No signalling is allowed between the dwarves — they cannot meaningfully pause before answering, for instance — but they do have a night in a communal cell in which to agree the optimum strategy. How many dwarves can be certain of going free if the best strategy is –adopted?
This question was set to my daughter as homework.
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