The math puzzle at the end of my July diary was as follows.

Of two unknown integers, each between 2 and 99 inclusive, a person P is told

the product and a person S is told the sum. When asked whether they know

the two numbers, the following dialogue ensues:

P: “I don’t know them.”

S: “I knew that already.”

P: “Then I now know the two numbers.”

S: “Then I now know them, too.”

What are the two numbers? Prove that your solution is unique.

Here is Prof. Dijkstra’s solution … though I think it

can be done with fewer words.