Two whole numbers, m and n, have been chosen. Both are greater than 1 and the sum of them is less than 100. The product, m × n, is given to mathematician X. The sum, m + n, is given to mathematician Y. Then both mathematicians have the following conversation:

X: "I have no idea what your sum is, Y."
Y: "That's no news to me, X. I already knew you didn't know that."
X: "Aha! Now I know what your sum must be, Y!"
Y: "And now I also know what your product is, X!"

The question: What are the numbers m and n?

The answer: Click here!

Another question: Thanks to Yiheng Wang, we can present you the following puzzle:

There is a professor with three of her equally highly intelligent students (Amy, Brad, and Charles) and they are playing a puzzle game. The professor puts a piece of paper on each student's forehead, and on each piece of paper, there is a positive integer number. Each student can see the numbers on the other two students' foreheads, but not the one on him/herself. The professor tells the students: out of these three positive integer numbers, one number equals to the sum of the other two.

The students cannot speak until the professor starts to ask question and the three students answer in order.
Professor: "Do you know the number on your forehead (for sure, no guessing)?"
Amy: "I don't know."
Brad: "I don't know."
Charles: "I don't know."

Then the professor starts the second round of questioning.
Professor: "Do you know the number on your forehead (for sure, no guessing)?"
Amy: "I don't know."
Brad: "I don't know."
Charles: "Yes. It's 144."

Question to you, the reader: what are the three numbers?

Another answer: Click here!