1 <x <100
1 <y <100
Since Mr. Product can’t figure out the #s, then the product of x*y has multiple factors and x & y can’t both be prime #s.
How would Mr. Sum know that Mr. Product wouldn’t know the #s?
I dunno.
Mr. Sum knows the sum of x+y. The sum cannot be even, since all positive even integers can be expressed as the sum of 2 prime #s. (TRY IT, you’ll see, and that will be your fun for this summer…)
Therefore, the sum must be odd.
If the sum is odd, then one number is odd and the other is even.
(TRY IT, you’ll see, and that will be more fun for you this summer…)
If one # is odd & the other # is even, then the product must be even.
(TRY IT, …ok, you know this by now 🙂 )
So what we have so far:
– X&Y are not both primes
– x+y is odd
– x is odd & y is even (or vice-versa)
Now it’s trial & error (mostly error…)