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?

<< what about for example 2,4?
even if 2 and 4 are not both prime,
a product 8 implies the pairs 2 and 4,
meaning they are not possible either. >>

<< it seems youre assuming goldbach´s conjecture here.. the fact that the sum of two primes is
even does not imply all even numbers are the
sum of two primes.. (maybe i didnt understand
correctly) >>

In the first case, I am not eliminating all the possibilities. Yes there are other pairs that can be eliminated, but that can wait until we've narrowed the field as much as we can with broader deductions.

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.

Posted by TomM on 2002-10-16 04:46:13