[Guest]

You and your two best friends have numbers written on your foreheads. You are told that the three numbers are primes and that they form the sides of a triangle with prime perimeter. You see 5 and 7 on your friends' forehead, both of whom state that they cannot deduce the number on their own foreheads. What number is written on your forehead?

[Guest]

You and your two best friends have numbers written on your foreheads. You are told that the three numbers are primes and that they form the sides of a triangle with prime perimeter. You see 5 and 7 on your friends' forehead, both of whom state that they cannot deduce the number on their own foreheads. What number is written on your forehead?

hokay, so buddy A has a "5" written across his forehead, buddy B has "7" written across his...

that I have a number between 3-11,either 5, 7, or 11... which would give me a total of 17, 19, or 23...

If my life depended on it, I would die as I am very unlucky, much like Hurley from LOST o.O

I also didn't pay much attention in math class, so I may be off by a wee little bit

[Guest]

Assuming you can't have a duplicate of the other numbers, it would have to be 11.

Duplicates are allowed as far as they do not violate the other properties of the puzzle.

Edited April 8, 2008 by brhan

[Guest]

.....

So, your numbers can be 5,7, or 11.

What happened to your friend A

he sees b=7, c=5 or 7 or 11,

When c=7, a<14

a=1, it follows the rule of triangle, but a+b+c=15 is not prime

a=2, a+b+c=16

a=3, as it follows the rule of triangle and a+b+c=17 is prime

a=5, as it follows the rule of triangle and a+b+c=19 is prime

So, according to A, his numbers can be 1,3, or 5.

So, lets think about B

What happened to your friend B

he sees a=5, c=5 or 7 or 11,

When c=5, b<10

b=1, as it follows the rule of triangle and a+b+c=11 is prime

b=2, it follows the rule of triangle , but a+b+c=12

b=3, as it follows the rule of triangle and a+b+c=13 is prime

b=5, a+b+c=15

b=7, as it follows the rule of triangle and a+b+c=17 is prime

So, according to B, his numbers can be 1,3, or 7.

In the first highlighted sentence above you said A's number can be 1, 3 or 5. Well, 1 is not considered as a prime number (at least in this puzzle) and you may check my post #21 above how 3 can be eliminated. So definitely A will know his number is 5. As a result you know your number is not 5 because your friend (in this case A) managed to know his number.

For the second highlighted sentence 3 can be eliminated as follows leaving B's number to be 7 (as I said above 1 is not considered as a prime number in this puzzle). Since A sees (7, 7) and concludes he has 3 or 5. But if he has 3 then he reasons that person B sees (7, 3) and would know his number is 7. Since A doesn’t know his number, then A would conclude he has a 5. As a result you eliminate that from the possible solutions since B doesn’t draw this conclusion.

So your number must be 11.

Edited April 8, 2008 by brhan