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?
my doubt as to the 1 and 100 issue came from
the fact that it seemed to me the problem
was much richer in the not inclusive case.
some questions as to TomM´s analysis:
"1 The numbers are not both prime, or Alan, knowing their product, would know the 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.
"2. Bob knew that they could not both be prime. Since the sum of any two primes is an even number, unless one of the primes is 2, then the sum Bob knows must be odd.."
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)
anyway my personal guess is the pairs are
13 and 4, totalling 17 and product 52..
guess
