Alan and Bob are trying to figure out two numbers. They know that both numbers are integers between 1 and 100 (but not 1 or 100). Alan knows the product of the numbers, and Bob knows the sum. Their conversation goes as follows:
Alan: I can't tell what the two numbers are.
Bob: I knew you couldn't.
Alan: Ok, now I know the numbers.
Bob: Now I know them, too.
What are the two numbers?
(In reply to
re: guess by TomM)
"In the second case, if the sum is even, Bob would have to know that there is no pair of primes that add to that number. My point is that Bob knows that the two numbers are not both prime. Since Goldbach's conjecture is neither proven nor disproven, Bob would not know that. Therefore the sum is odd."
i disagree:
"Bob would have to know that there is no pair of primes that add to that number."
bob could easily know this even though GB conjecture is
a conjecture. its just a matter of checking the n/2
possibilities..
(incidentally, the number is odd, but only because GB
conjecture holds at least up to 100 :)
re(2): guess
