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?

I just started writing down prime numbers to see if they fit:

3: 3+5+7=15=not prime

5, 7: these can't work because if either of the other two people see the same number on 2 foreheads, they'll be able to work out the answer.

11: 5+7+11=23=prime, OK

the unknown side can't be any larger than 11 because then the combo of sides won't make a triangle, so this has to be the answer.

does seem too easy though.

Posted by lauren on 2005-03-11 17:42:13