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?

11, Maybe I am missing something.  Seems too easy.

If the others have 5,7 prime sides of a prime triangle, the only other possible combinations is 3,5,7=15 not prime.

The reason they cannot tell their numbers is that they could each see the 5,7,11.  One could also see 7,11,13.  And the other could also see 5,11,13.  But you did not need this to solve the problem.

 

Edited on March 11, 2005, 5:31 pm

Edited on March 11, 2005, 5:41 pm

Posted by john on 2005-03-11 17:28:25