Two integers x and y are selected such that 1 > x >= y > 100. Player A is given the product x*y and player B is given the sum x+y. The following dialogue takes place:h/t: Redditer Vitanza
A: I don’t know the values x and y.
B: I knew you didn’t know. I don’t know them either.
A: Now I know x and y.
B: Now I know them too.
What are x and y?
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Answer:
ReplyDeleteFirst comment means number can't be the product of two primes.
Second comment FIRST means that the number can't be split into two primes, because otherwise, it would be possible that A would have already known. Since all even numbers (save 2) are a sum of two primes, this means the sum must be odd, and rules out some other options. SECOND means that the number can't be two greater than a prime.
Third comment means that of all of the possible sums, only one splits to two numbers that can multiply to A's product.
Fourth comment is self-explanatory, but I don't know of a way to do it beyond cutting possibilities down to one.