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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.

What is the number written on your forehead?

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

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 Solution | Comment 86 of 89 |

My Solution is there is no solution and here is why. Pythagorean theorem says that a squared + b squared = c squared.  We know 2 parts of it which is 5 and 7.  since 7 is bigger then 5, 5 can not be the hypotnuse which leaves 2 ways the problem can be done.

5(5) + 7(7)=c squared

25+49=c squared

74=c squared

not a prime answer

or

5(5) + b squared=7(7)

25+ b squared=49

-25                  -25

b squared=24

b= not a prime number

Therefore there is no solution

 Posted by Briana on 2005-04-23 02:35:31
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