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?
We know that in any triangle the two shortest sides must have a combined length greater than the remaining side. We also know that the third side in this particular problem must be prime. A remaining side of 11 meets the requirements of the problem. The total three sides form a viable triangle, each side of which is a prime number (5, 7, and 11) and the total permiter of the triangle is also prime, 23.