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?

I'd forgotten about the possibility of p(1) being not a prime, but 1! That changes Bob's figures all around, as you've already indicated.

Alan's figure is the product of two primes. but because Bob's sum still must be odd, if one of the primes is 2, the other must be 2. This gives us 1 and 4

Now all we have to do is show that for any two odd primes ≤ 100, p(1) and p(2), there is another pair of odd primes p(3) and p(4) such that p(1) + p(2) = p(3) + p(4)

Posted by TomM on 2002-10-15 04:05:09