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 re: full solution by Charlie)

Charlie, I think you are making confusion when you say "the puzzle never states that the narrator made clear to the others that HE wasn't...".

The narrator is not one of the three persons, you are, and you are seeing a 5 and a 7. And it is tacitly stated (by the narrator) :  "both of the other people agree that they cannot deduce the number on their own foreheads".

My solution tries to prove what would be MY (one of the persons, that it is seeing a 5 and 7) reasoning, to deduce MY number.

(Sorry for possible mistakes in my english, I'm brazilian).  

Posted by pcbouhid on 2005-03-11 21:02:34