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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)

Comments: ( Back to comment list | You must be logged in to post comments.)
 I just joined today; may I take a shot? | Comment 14 of 20 |

I tend to think it's a sequence of --

Bob = N

Chuck = N x 2 + 1

Adam = N x 3 + 2

If this is true, Adam = 563; Bob = 1127, and Adam = 1691.

This is probably way to simplistic of a solution, but logic isn't supposed to require a lot of higher math knowledge, so I thought I'd take a guess.  Please be gentle - I'm new to the group.

Vickie

 Posted by Vickie on 2006-08-18 17:33:11

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