Puzzling puzzle, can anyone shed some light?! Watch

smilee172
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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?


I came across this riddle/puzzle on a website, but as far as I could see there was no answer! Just wondering if any of you clever people on here could figure it out!
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LouE3D
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(Original post by laurah)
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?


I came across this riddle/puzzle on a website, but as far as I could see there was no answer! Just wondering if any of you clever people on here could figure it out!
Well, if 2 of the numbers on the hats added together quals the number on the other hat, then surely the answer can be 845.5?? it isn't a very good puzzle as there could be hundreds of answers (unless I'm missing something :confused: ) i.e 1 & 1690....
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a_man_1066
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Er... I'm sure someone who studies logic and that can probably prove this, but it seems that it's unsolvable.... I mean, why do they say "I do not know the number on my hat" so many times - are you sure its not a typo/misprint and that they are meant to say something different.
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**Pinx**
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oooya am well confused :s
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smilee172
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(Original post by a_man_1066)
Er... I'm sure someone who studies logic and that can probably prove this, but it seems that it's unsolvable.... I mean, why do they say "I do not know the number on my hat" so many times - are you sure its not a typo/misprint and that they are meant to say something different.
Nope that';s how it was displayed on the website, I really don't understand it but maybe the number of times they say 'I don't know..' is some kind of code or something. Really confused!
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frazer_1
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well, it involves some pretty complex logic reasoning, but the other two hats are 1045 and 646. And there is a reason why there are nine 'I dont know' answers


Think of this simple one to get you on the right wavelength:

If A was 6, B was 4, and C was 2

A's first response would be 'I dont know' as he could be either 6 or 2
B's first response would be 'I dont know' as he could be 4 or 8
C's first response would be 'I dont know' as he could be 10 or 2

As B said 'I dont know', A therefore knows he cannot be 2, as if he was 2, B would have said 4 straight away as A and C would both have been 2 and so B would have known he was 4 as he cannot be zero. Therefore, on his second response, A will say 6
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rufus_da_bear
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(Original post by frazer_1)
well, it involves some pretty complex logic reasoning, but the other two hats are 1045 and 646. And there is a reason why there are nine 'I dont know' answers


Think of this simple one to get you on the right wavelength:

If A was 6, B was 4, and C was 2

A's first response would be 'I dont know' as he could be either 6 or 2
B's first response would be 'I dont know' as he could be 4 or 8
C's first response would be 'I dont know' as he could be 10 or 2

As B said 'I dont know', A therefore knows he cannot be 2, as if he was 2, B would have said 4 straight away as A and C would both have been 2 and so B would have known he was 4 as he cannot be zero. Therefore, on his second response, A will say 6
i can't believe im going to do an AS in critical thinking. although on reading this for the 5th time, it makes a bit more sence
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