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Prime Perimeter (Posted on 2005-03-11) Difficulty: 3 of 5

You and two other people have numbers written on your foreheads. You are all told that the three numbers are primes and that they form the sides of a triangle with a prime perimeter. You see 5 and 7 on the other two heads and both of the other people agree that they cannot deduce the number on their own foreheads.

What is the number written on your forehead?

See The Solution Submitted by Erik O.    
Rating: 2.8235 (17 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): Trying to solve this... | Comment 40 of 89 |
(In reply to re: Trying to solve this... by pcbouhid)

Well, I try not to critique every solution I disagree with, or I wouldn't have any time for schoolwork and stuff.  Also, my attention span is not long enough to read every comment thoroughly when there are over thirty.

But if you would like more details on why I disagree with your solution, you will receive it.

" If my number is a 5, the one that have a 7 will reason : "I'm seeing two 5's, and so my number is a 3 or a 7 (remember the prime perimeter). If my number is a 3, then the other two could deduce that both have a 5, since if one of them had a 3, the other would know that he had to have a 5. Since no one announced his number, my number is not a 3, so my number is 7". Since the one that have a 7 didn't say nothing, my number is not a 5."

The one part I disagree with is underlined.  As I interpreted the problem, I am not part of the conversation in which the "other people agree that they cannot deduce the number on their own foreheads."  I might as well be asleep while they are talking.  The underlined sentence, had I written it, would be replaced with "If my number is a 3, then the other awake person would not be able to deduce his number, since he might think he has a 3.  Perhaps if the sleeping person were awake, and couldn't figure it out, I would know my number to be a 7."

There is something to be said here about multiple interpretations.  Under your interpretation, your solution is absolutely correct, while mine is incorrect.  Under my interpretation, it is the other way around.  It would seem your interpretation must be correct since it offers a unique solution.  However, do you think that an interpretation of a problem is correct just because it leads to a more satisfying solution?  If my interpretation led to a unique solution while yours did not, would that be reason enough to accept mine?

The big authority over which interpretations and solutions are correct is the author, Erik O.  I don't hold anything against him, since it is impossible, and not worthwhile to eliminate every trace of ambiguity.  I'd like to hear what he has to say.  We could both be wrong.

  Posted by Tristan on 2005-03-13 22:06:15
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