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 A solution by Pat Whitaker)

Pat, you wote :

"If I had an 11 then then the fellow with the 7 would see 5 and 11.  leaving only the choices of 3 or 7 for his number. Since the triangle 3,5,11 is impossible 7's owner would be able to determine his own number."

I stopped  to read your solution at this point, because the fellow with the 7, seeing 5 and 11, could have a 13 (that is prime) and 5 + 11 + 13 = 29, also a prime (perimeter), so, he is in doubt if he has a 7 or a 13.

Posted by pcbouhid on 2005-04-05 16:07:25