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)

I agree that my number could only be 5, 7, or 11. These are the only solutions to the constraints that the sum of three primes (5, 7, x) is also a prime and that the three numbers are also the length of the sides of a triangle.

I just don't follow your reasoning in eliminating 5 and 7.

 

Posted by Mike on 2005-03-11 22:41:05