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?

assume you have 11 on your head, so the guy with the 7 on his head sees 11 and 5, he adds 11 and 5 and gets 16. The next prime greater than 16 is 17, however the difference 1 is not prime, the next prime thereafter is 19,  the difference 19-16=3, could be on your head (blowing the exclusivity of the initial assumption) . The prime greater than 19 is 23, which is 7 greater than 16, therefore 11+5+7=23.

the solution could be 3 as well as 11.

Posted by emdad on 2005-03-14 22:04:02