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Prime Perimeter (Posted on 2005-03-11) Difficulty: 3 of 5

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?

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

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re(3): Trying to solve this... | Comment 41 of 89 |
(In reply to re(2): Trying to solve this... by Tristan)

Ok, let's give the word to Erik !!!

I presented MY solution based in the following facts, explicit or not :

1) I'm the person who are seeing a 5 and a 7.

2) All the three persons are equally inteligent, and the reasoning that I made could be the reason that each of the other two would make if they were seeing a 5 and a 7.

3) I arrived at my conclusion only (and ONLY), after a lapse of time, neither of the two announced that were able to give an correct answer (in fact, they both were in doubt). My conclusion was based in the fact that what the other two were seeeing didn't lead them to certainty.


The part you disagree with : "I'm seeing two 5's, and so my number is a 3 or a 7 (remember the prime perimeter). If my number is a 3, then the other two could deduce that both have a 5, since if one of them had a 3, the other would know that he had to have a 5. Since no one announced his number, my number is not a 3, so my number is 7". 

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.

BUT HE (who have a 7) DIDN'T ANNOUNCE HIS NUMBER, what could be done if he were seeing two fives !! So, he's not seeing two fives, just seeing one five (like me) !! SO I CERTAINLY DON'T HAVE A 5.

Similar reasoning would make the person who have a 5, IF I HAD a 7.


  Posted by pcbouhid on 2005-03-13 23:22:34
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