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?

...really not quite sure yet, but could this puzzle have multiple solutions? I believe the conversation is possible for the following values on Bob's and Chuck's hats:

Bob = 356  , Chuck = 1335
Bob = 623  , Chuck = 1068
Bob = 646  , Chuck = 1045
Bob = 712  , Chuck = 979
Bob = 979  , Chuck = 712
Bob = 1068 , Chuck = 623
Bob = 1246 , Chuck = 445

Avin, is one of these the solution you are after?

Posted by JLo on 2006-08-14 20:50:55