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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): THERE IS NO SOLUTION! | Comment 82 of 89 |
(In reply to re(2): THERE IS NO SOLUTION! by jon)

"if the 5 thinks hes a five, hes looking at 7 and 17. His equation is 5+7+17=29, which is prime. but he can assume that he's a 7 along with the 7 and have the equation 7+7+17=31."

You can't draw a triangle with sides 5, 7, and 17.

"the same thing goes for #7. When the seven thinks he's a seven the only thing he sees is  the 5 and the 17, so his equations can be 7+5+17=29 or 19+17+5=41."

You can't draw a triangle with sides 5, 7, and 17.

And I wasn't saying they would tell the other what they saw, I was just saying they could gather information from the other's silence.

  Posted by Dustin on 2005-04-09 02:55:50
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