 The Sum and Product Puzzle is like the Sum and Least Common Multiple Puzzle except that the allowable integers are taken in the range \(2,\dots,100\) (inclusive), Mr. L is told the product of the two numbers (instead of their least common multiple), and the dialogue is altered slightly (L: “I don’t know the numbers”, S: “I knew you didn’t know them”, L: “Ah, but now I do know them”, S: “And now so do I!”). These changes result in a substantially more difficult problem. See Plaza (1989, 2007) for details. 