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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(2): THERE IS NO SOLUTION! | Comment 81 of 89 |
(In reply to re: THERE IS NO SOLUTION! by Dustin)


if five thinks he's a 5, and seven sees a 5 and a 17, there is no way that without conversing they can just deduce what their numbers are.

if the 5 thinks hes a five, hes looking at 7 and 17. His equation is 5+7+17=29, which is prime. but he can assume that he's a 7 along with the 7 and have the equation 7+7+17=31. No other options work for the man with the #5 on his head. He can't assume anything else, because nothing else works for him. Therefore, since he has two possibilities he is unsure .

the same thing goes for #7. When the seven thinks he's a seven the only thing he sees is  the 5 and the 17, so his equations can be 7+5+17=29 or 19+17+5=41. Now if #5 and #7 are asking each other if their numbers are correct that's not deducing anything.

It's not a deduction if they are giving each other the answers, and unless they do that, the other two can still assume that there is more than one number that can apply. Therefore, it's not possible.

If five sees the 7 and 17 he has to assume that he's a number that makes that prime. The numbers that work are 5 and 7. therefore he's uncertain, just like if seven sees the 5 and 17 he can think he's a 7 or 19.

If they knew what they were, the riddle collapses, because he states to us that they can't. Five CANNOT tell you he is five and seven CANNOT tell you that he's seven. it doesn't matter what five thinks because he can't tell seven taht he's 7. and vice versa.

While five thinks he's 5, seven can see the 5 and 17, but the only thing he can think is the two equations that make it work, which means it won't work for him... he can still think hes a seven or a nineteen.

  Posted by jon on 2005-04-09 01:30:25

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