"Head sums Ade, Binky, and Carl are honest perfect logicians. A hat is placed on each of their heads. Each hat has a whole number larger than zero written on it, which the other two logicians can see but which the wearer cannot. One of these numbers is the sum of the other two (so for example, the three numbers could be 3, 7, 4, or another possibility is 6, 6, 12). All of this is public knowledge."
"Ade says for all to hear: I do not know the number on my hat Binky then announces: I do not know the number on my hat Ade then announces: I know the number on my hat! What number is on Ade's hat? I'll be back at 5pm UK with the solution. PLEASE NO SPOILERS. Please discuss hats. The puzzle was devised by Timothy Chow, inspired by a puzzle by Dick Hess."
Ade, Binky, and Carl wear hats labeled with positive integers and one number equals the sum of the other two. Ade sees Binky = 3 and Carl = 1, so Ade's possibilities are 4 (3+1) or 2 (3-1), and Ade initially does not know his own number. Binky, after hearing Ade, still does not know his number. Binky's continued ignorance rules out the possibility that Ade's number is 2, because if Ade were 2 Binky would deduce his own number. Using these eliminations and common-knowledge reasoning, Ade concludes his number is 4. All reasoning assumes honest perfect logicians and common knowledge of statements.
Read at www.theguardian.com
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