Mr. S. and Mr. P.

October 23, 2009

John McCarthy, who discovered Lisp, attributes this puzzle to Hans Freudenthal:

We pick two numbers a and b, so that 99 ≥ ab ≥ 2. We tell Mr. P. the product a × b and Mr. S. the sum a + b. Then Mr. S. and Mr. P. engage in the following dialog:

Mr. P.: I don’t know the numbers.

Mr. S.: I knew you didn’t know. I don’t know either.

Mr. P.: Now I know the numbers.

Mr. S.: Now I know them too.

Find the numbers a and b.

Your task is to find the two numbers. When you are finished, you are welcome to read or run a suggested solution, or to post your solution or discuss the exercise in the comments below.

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