It's a conversation that builds slowly, as only good logical problems do. Each sentence does not provide new information: it erases possibilities.
Sum and product
Riddle statement
Two different integers \(x\) and \(y\) satisfy \(2 \le x < y \le 99\).
One person is told the sum \(S=x+y\), and the other person is told the product \(P=xy\).
Conversation:
1. Product: “I don't know what the numbers are.”
2. Sum: “I already knew it.”
3. Product: “So now I know.”
4. Add: “Then I know them too.”
What are \(x\) and \(y\)?