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?

(In reply to full solution by pcbouhid)

pcbouhid, I think your solution is a nice piece of work.

I have been working around the same line of thinking but never managed to get it solved completely.  As for Charlie's remark about the solution being over sophisticated, I don't think so.  Both people have the time to discuss and after this discussion they agree that they cannot deduce the number.  So there is enough time to complete your reasoning.  And the reasoning does only depend on the fact that they do not anounce their proper numbers immediately following their discussion, not on any morre remarks/actions made later.  

Posted by Hugo on 2005-03-11 21:41:05