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What are the numbers "m" and "n" in this conversation?

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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!"
posted Apr 21, 2014 by Ashwini Miraj

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