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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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Semi-Solution? | Comment 2 of 89 |

I just started writing down prime numbers to see if they fit:

3: 3+5+7=15=not prime

5, 7: these can't work because if either of the other two people see the same number on 2 foreheads, they'll be able to work out the answer.

11: 5+7+11=23=prime, OK

the unknown side can't be any larger than 11 because then the combo of sides won't make a triangle, so this has to be the answer.

does seem too easy though.

  Posted by lauren on 2005-03-11 17:42:13
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