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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: ( Back to comment list | You must be logged in to post comments.)
exponents? | Comment 2 of 20 |

the numbers couldnt be positive integers because if the number of the other two hate would need to be smaller than that of adams hat. so if chucks hat (for example) is equal to the sum the other hats then his hat would have to be larger than 1691 (adams number).negative integers would have to be used , however , it is said that all of the numbers are positive integers.

i have a feeling that exponents are used ....?  comment back if u dont know what i mean

 


  Posted by nick on 2006-08-15 00:51:13
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