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): Trying to solve this... by pcbouhid)

pcbouhid, I understood your solution.  But with your new explanation, I have a better opportunity to pinpoint exactly where we disagree.

"THIS IS THE REASONING OF THE PERSON WHO HAVE a 7, IF I HAD a 5 ! He, seeing two fives, would deduce that his number could only be 3 or 7 (because 5 and 11 would make the perimeter composite). And he continues thinking : But if I had a 3, each of the other two (who have fives) were seeing a 3 and a 5, and could deduce that its number (greater than (5-3) and less than (5+3)), could only be 5, and announce their numbers. Since no one is saying nothing, my number could only be 7."

I disagree with the underlined part.  If a person sees both a 3 and a 5, his own number can be a 3 or a 5.  You argue that if his number were a 3, then someone must be seeing two 3s.  This brings me to my main disagreement.  If I were the one seeing two 3s, I would not say anything.  I will not announce whether I know my own number until the very end.

My objection is the same as Charlie's, just so you know.

Posted by Tristan on 2005-03-14 00:50:01