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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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 Triangles and Primes - | Comment 18 of 89 |

We know that in any triangle the two shortest sides must have a combined length greater than the remaining side.  We also know that the third side in this particular problem must be prime.  A remaining side of 11 meets the requirements of the problem.  The total three sides form a viable triangle, each side of which is a prime number (5, 7, and 11) and the total permiter of the triangle is also prime, 23.

Gordon S.

 Posted by Gordon Steel on 2005-03-12 00:56:14

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