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 Semi-Solution? by lauren)

"5, 7: these can't work because if either of the other two people see the same number on 2 foreheads, they'll be able to work out the answer."

I don't understand this.  If I have a 5 on my forehead also, the guy with the 7 will see two 5's, and not know if he himself has a 3 (to make 13) or a 7 (to make 17).  And the guy with the 5 on his head (besides me, in this case), would be in the same condition as myself.

Likewise, if I had a 7, the guy with the 5 wouldn't know if he had a 3 or a 5 (to make 17 or 19), and the guy with the 7 would be in my position.

Posted by Charlie on 2005-03-11 18:26:51