What The Students Know Puzzle - Solution

The Puzzle:

What The Students Know
A teacher says:

"I am thinking of two natural numbers bigger than 1. Try to guess what they are."

The first student knows their product and the other one knows their sum.

First: "I do not know the sum."
Second: "I knew that. The sum is less than 14."
First: "I knew that. However, now I already know the numbers."
Second: "And so do I."

What were the numbers?

Our Solution:

The numbers were 2 and 9. Why? Try to think about it.

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