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?
(In reply to
re: THERE IS NO SOLUTION! by Dustin)
um...
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 20050409 01:30:25 