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 Logicians, hats, and numbers (Posted on 2006-08-14)
Adam, Bob, and Chuck, three perfectly intelligent logicians, are sitting facing each other with a hat on each of their heads so that each can see the others' hats but they cannot see their own. Each hat, they are told, has a (non-zero) positive integer on it, and the number on one hat is the sum of the numbers on the other two hats. The following conversation ensues:

Adam: I do not know the number on my hat.
Bob: I do not know the number on my hat.
Chuck: I do not know the number on my hat.
Adam: I do not know the number on my hat.
Bob: I do not know the number on my hat.
Chuck: I do not know the number on my hat.
Adam: I do not know the number on my hat.
Bob: I do not know the number on my hat.
Chuck: I do not know the number on my hat.
Adam: The number on my hat is 1691.

Adam was correct. What are the numbers on the other two hats?

 No Solution Yet Submitted by Avin Rating: 3.7778 (9 votes)

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 Guys, seriously | Comment 18 of 20 |
Hey everyone
I'm sure there is a perfectly logical explanation for this, but in my mind one problem remains - when a guy looks at two numbers, two people saying "I don't know" a couple of times doesn't imbue him with psychic powers as to whether those two numbers are the sum and a smaller number or the two smaller numbers. Is there some kind of 'logic puzzle thinking' that I'm just not used to or some kind of kooky assumed knowledge in the wording of the puzzle?
It seems like a load of posted suggestions so far rely on a lot on drawing conclusions from this magical phrase "I don't know"... I can't wait to see what the thinking is behind the solution, but I hope it's based on something that would work more in the real world!

 Posted by Ben on 2006-09-07 18:08:45

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