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?
(In reply to
re(3): full solution as understood by Sachin)
The only possibility of Scenario 1. being not possible is
If B and C both get a value of 3. Then the only possible value of A is
5. So A, would have guessed his number immediately. But question does
not state whether B or C know that initially A was not able to guess
the number.
If the question means that all of them know that all were not able to guess their number initally then the answer is 11.
Otherwise it could be both 5 or 11.
Erik please clarify.

Posted by Sachin
on 20050312 05:10:38 