The Head of Quant research meets two junior (A and B) quants to announce their bonuses (expressed in k$). They now that they are between 2 and 100. He gives the product to A and the sum to B. A says: "I don't know what are the two bonuses"B replays: "I knew you would not know"Then A says: " Now I know!"And B says: "I know too!"What are the two bonuses?

13 and 4 (product and sum 52 and 17, respectively).Solution on the attached notebook.

That's right!I did it using Excel after reducing the possible sums to {11,17,23,27,29,35,37,41,47,53} which makes the solution much easier

just to add some reference: this is so-called "the impossible problem". the version above should be the original one from Freudenthal and Sprows, and i remember the upper limit of the two numbers could be extended to 800+, which still guarantees the unique solution (already given above).there is an interesting story about this problem due to Gardner (again!). he gave a version with an upper limit of 20 (see below), and later on he claimed it was literally impossible... or so he thought. Lee Sallow later on found a unique solution to this "impossible problem". can you find the solution?here is Gardner's december 1979 formulation:Two numbers (not necessarily different) are chosen from the range of positive integers greater than 1 and not greater than 20. Only the sum of the two numbers is given to mathematician S. Only the product of the two is given to mathematician P.On the telephone S says to P: "I see no way you can determine my sum."An hour later, P calls back to say: "I know your sum."Later S calls P again to report: "Now I know your product."What are the two numbers?