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 Erick Please Clarify by Sachin)

I concur.  The lack of a unique solution indicates that my interpretation was incorrect.  If the first two people expected me to speak up if I could figure it out, then there would be a unique solution.

...or so it may seem.  If I were part of their conversation in which they agreed that they couldn't figure it out, then I would have said after a little while that I could figure it out.  After this, the other two would no longer be agreeing that they can't figure it out, but rather agreeing that they can figure it out.  Since this didn't happen, no solution remains.

It seems we should assume that I only say at the beginning that I cannot figure it out.  But why assume that I am part of the conversation only at the beginning?

Posted by Tristan on 2005-03-13 02:10:23