October 23, 2009
John McCarthy, who discovered Lisp, attributes this puzzle to Hans Freudenthal:
We pick two numbers a and b, so that 99 ≥ a ≥ b ≥ 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.