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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(4): full solution as understood | Comment 26 of 90 |
(In reply to re(3): full solution as understood by Sachin)

The only possibility of Scenario 1. being not possible is

If B and C both get a value of 3. Then the only possible value of A is 5. So A, would have guessed his number immediately. But question does not state whether B or C know that initially A was not able to guess the number.

If the question means that all of them know that all were not able to guess their number initally then the answer is 11.

Otherwise it could be both 5 or 11.

Erik please clarify.

  Posted by Sachin on 2005-03-12 05:10:38

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