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 full solution by pcbouhid)

From what I have understood from pcbouhid solution. There are three possible numbers for,say for  A as 5,7,11. Let say B has 5 and C has 7.

Scenario 1. A=5, B =5 and C =7

In this case C will see 2 fives which means the only possible values for C are 3 or 7. If C's value is 3, B could have guessed his numbers as he is seeing 3 and 5, and only possible third number is 5. But B couldn't, which leaves C's number as 7. Since even C could not guess his number as 7. So scenario 1 is not possible.


Scenario 2. A = 7, B =5 and C =7

In this case B will see 2 sevens which means the only possible values for B are 3 or 5. If B's value is 3, C could have guessed his number as he is seeing 3 and 7, and only possible third number is 7. But C couldn't, which leaves B's number as 5. Since even B could not guess his number as 5. So scenario 2 is also not possible.

So we are left with the only possible values of A = 11, B =5 and C =7.

So the number is 11.

Edited on March 12, 2005, 2:12 am

Edited on March 12, 2005, 2:13 am

Edited on March 12, 2005, 2:17 am

Posted by Sachin on 2005-03-12 02:00:00