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Question
The Moonstone, a fabulous gem, has been stolen again. Witnesses saw one person steal it, but cannot describe him (or her) at all, nor has any physical evidence been found. Police suspect one of the three most notorious jewel thieves may be responsible and have all three under close surveillance - including telephoto lenses and paraboloidal microphones - but lack a reason to arrest any of them. Each suspect, denying involvement in the theft, has expressed curiosity: Who took the Moonstone this time?
Later, the three were observed dining together. Each had occasion to leave the table and visit the lavatory and during their absence, the two at the table flipped a (presumably fair) coin, hiding its face from the absentee (and from the surveillance team), but not from each other. After the third suspect returned from the lavatory, all three winked at each other and dispersed silently. The surveillance team saw only the back of one suspect’s head when he winked, so his wink was not recorded. The surveillance team says all three suspects know that one of them stole the gem but, if one did not, he didn't know which one of the other two committed the crime; and the surveillance team does not know either. How was all this information communicated?
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First thief sees two heads, or two tails and doesn't see the third flip that has to be one or the other. Going from that, the rest of the 2 thieves should blink the same eye. If they blink different eyes, one of them is the thief, but not knowing if the flip is heads or tails, first thief does not know which of the two is the thief, only that one of them is. If the first thief sees heads and tails, the other two should blink different eyes if neither of them is the thief, but the same eye if one of them is the thief. Basically, not knowing the third flip, he doesn't which one it is. All three then know whether or not one of them stole the gem, but only the one that actually stole it knows it was him. The police surveillance team listens to the conversation, knows that the thieves know, but because they didn't see the flips, nor which way the third thief blinked, they don't know if it was one of the 3 or not.
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