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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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Solution THERE IS NO SOLUTION! | Comment 79 of 89 |
I know this sounds crazy, but i will take some time to explain this to you...

we know we can't have a 3, because 7+5+3=15, which isn't prime. We know that it's not 5 or 7, because if seven or five sees a seven or five the equation flops. Here's why it flops...

Say five sees a five on us, and the seven, he has the same equation in front of him as we do, which means that either, he can solve it because he has what we have, or the equation is not solveable.

Now say that seven sees a seven and a five. Then he is also in the same position as the person with the five on his head. Either he CAN solve it or no one can.

So by these rules, neither 5 nor 7 can be used, and neither can 3.

But maybe we should try to attempt to figure it out ourselves right?

Well, Let's assume that we have an 11. If we have an 11 then the seven debates the seven or a thirteen. 7+ 11+ 5 = 23 and 13+ 11+ 5 = 29, so seven couldn't figure it out with that number.

Neither can five. Five sees the eleven and the seven and can assume that either he's a five, 5+11+7=31, or that he's another eleven, 11+11+7=29. So eleven is one number that works

Another number that works is 17. The reason is this. It is another number where no one else can figure it out but you. The person with the 5 can assume he has a 5 or a 7, and the person with a 7 can assume he has a 7 or a 19.  so...

if five thinks he's 5, then 5+ 17+ 7= 29, or if he assumes that he's a 7 then 7+17+7 = 31. Number 5 cannot know his number.

if seven thinks he's 7, then the 7+5+17=29, or if he assumes that hes a 19, then 19 +17+5=41. Number 7 Cannot know his number.

There is no answer to this riddle, because it contradicts itself. By telling us that they cannot deduce their number they really limited the riddle. I think generally the resolution is weak. Probably an ameature thinking it's cool to not have a resolution. Anyway, since we can have an 11 or a 17, we don't know our number. There is no solution to this riddle. That's gay...someone think this through a bit more...

  Posted by jon on 2005-04-09 00:11:17
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