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Math Guessing Game

Two whole numbers m and n have been chosen but are unknown. Both are unequal to 1 and their sum m + n is less than 100. The product m n is given to Student A. The sum m + n is given to Student B. Then both students have the following conversation:

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

The Question: What are the numbers m and n?


Hint: Think and ask good questions...could m or n be prime? Over 50? etc.

Then, role play the questions from the perspectives of both Student A and Student B.


Solution Commentary: Rather than provide a solution, I refer you to the web site where I found this problem. It includes several suggested aolutions. Are they correct?