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?

so the number on my head is a prime, and my number when added to the other two primes forms another prime number.
5 + 7 + x = prime perimeter
prime perimeter has to be greater than 13, as 5+7 is 12 and the next prime after 12 is 13, but the difference 1 is not prime, so x cannot be 1.
x must be one of a series of differences between all primes greater than 13 and 12.
x can be either; 17-12, 19-12, 23-12, 29-12, 31-12, 37-12, 41-12, 43-12, 47-12, 53-12...
The solution lies in working out the range of possible x's for the other two poeple and the conjuntion of the three should give you one remaining number, that being x.

Posted by emdad on 2005-03-14 21:37:39