I'm looking for one or more logic puzzles I've seen in the past that run something like the following: Some core information is given to two people, possibly the sum and product of two integers or some relation thereon. Rusty memory says maybe one person is given the sum, the other is given the product. Then two mathematicians iterate for awhile, A: I can't deduce the answer. B: Neither can I. A: I still can't deduce the answer. ... and after a few rounds of this one of them can deduce the answer. Can anyone supply some puzzles of this flavor? (without answer :-) Thanks, - Scott P.S.- The original wording was probably an ambiguous "I don't know the answer" rather than the more accurate "I cannot deduce the answer". I don't think the puzzle(s) actually specified mathematicians, but realistically nonmathematicians are unlikely to make the necessary deductions.