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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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to jason, why your answer is wrong | Comment 72 of 89 |
Although you had a good thought there with the prime perimeter clue, you left out one detail. The properties of a triangle (and this puzzle) dictate that your number be 3, 5, 7, or 11. You pointed out that 5 + 5 + 7 = 17, which is prime. However, you missed that 5 + 7 + 7 = 19, and 5 + 7 + 11 = 23, both of which are prime. This means that the only number eliminated by your method is 3. But we still need to figure out if we can tell which of the 5, 7, or 11 it is...
  Posted by Michael on 2005-04-04 12:00:27
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