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Logicians, hats, and numbers (Posted on 2006-08-14) Difficulty: 5 of 5
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
answerrupa2007-02-25 13:01:54
re: Guys, seriouslybumble2006-09-13 17:51:45
Guys, seriouslyBen2006-09-07 18:08:45
I've solve it!Hetman_elephant2006-09-06 05:12:37
Some ThoughtsIf only it was Chuck...Art M2006-08-24 21:16:43
SolutionNow if this doesn't convince everyone, I don't know...JLo2006-08-18 17:52:08
I just joined today; may I take a shot?Vickie2006-08-18 17:33:11
pool of numbersvj2006-08-17 09:02:35
Hints/TipsTake the downs with the upsGamer2006-08-17 02:00:17
Some ThoughtsNo wait, there are multiple solutions...JLo2006-08-16 17:23:58
Questionre: Perfectly IntelligentDej Mar2006-08-16 17:17:38
Solutionre: Perfectly IntelligentMat2006-08-16 13:19:29
re: Another shotAvin2006-08-16 09:30:37
SolutionPerfectly IntelligentGamer2006-08-16 01:25:55
Help needed.Vernon Lewis2006-08-15 19:40:32
Some ThoughtsAnother shotJLo2006-08-15 17:34:18
Ok, not much of a comment but...Ben2006-08-15 15:11:55
re: OK, I'll have a shot at it...Avin2006-08-15 09:30:12
exponents?nick2006-08-15 00:51:13
Some ThoughtsOK, I'll have a shot at it...JLo2006-08-14 20:50:55
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