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 Prime Perimeter (Posted on 2005-03-11)

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.

 See The Solution Submitted by Erik O. Rating: 2.8235 (17 votes)

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 re(4): Trying to solve this... | Comment 43 of 89 |
(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

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