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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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Some Thoughts re(2): A solution to Pat | Comment 77 of 89 |
(In reply to re: A solution to Pat by pcbouhid)

on another note, if I have a 5 on my head, the other guy with a 5 is seeing exactly what we are. This implies that he can solve it, it's not solveable, or you are wrong pat. I am saying you are wrong...

If he sees the 7 + 5, he's seeing exactly what we see. This means that he has the same problem as us. Now, under that assumption, you would have to say that if he can solve it, the equation doesn't work. You would also have to say that if he cannot solve it, which is what they say, if they cannot solve it with the same information as us, then we cannot solve it.

By these definitions, the number cannot be seven or five, because if I have a 7, the person with the 7 sees a total of 12 along with me, and if i have a 5 the person with 5 sees the same as me. No other person can be seeing the same as I or the equation doesn't work because then we can't solve it, or everyone can, makeing those #'s not fit the equation.

  Posted by jon on 2005-04-08 23:28:55

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