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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: ( You must be logged in to post comments.)
 Subject Author Date answer rupa 2007-02-25 13:01:54 re: Guys, seriously bumble 2006-09-13 17:51:45 Guys, seriously Ben 2006-09-07 18:08:45 I've solve it! Hetman_elephant 2006-09-06 05:12:37 If only it was Chuck... Art M 2006-08-24 21:16:43 Now if this doesn't convince everyone, I don't know... JLo 2006-08-18 17:52:08 I just joined today; may I take a shot? Vickie 2006-08-18 17:33:11 pool of numbers vj 2006-08-17 09:02:35 Take the downs with the ups Gamer 2006-08-17 02:00:17 No wait, there are multiple solutions... JLo 2006-08-16 17:23:58 re: Perfectly Intelligent Dej Mar 2006-08-16 17:17:38 re: Perfectly Intelligent Mat 2006-08-16 13:19:29 re: Another shot Avin 2006-08-16 09:30:37 Perfectly Intelligent Gamer 2006-08-16 01:25:55 Help needed. Vernon Lewis 2006-08-15 19:40:32 Another shot JLo 2006-08-15 17:34:18 Ok, not much of a comment but... Ben 2006-08-15 15:11:55 re: OK, I'll have a shot at it... Avin 2006-08-15 09:30:12 exponents? nick 2006-08-15 00:51:13 OK, I'll have a shot at it... JLo 2006-08-14 20:50:55

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