Laszlo has a Hungarian friend who makes up these number puzzles.  Often I find them quite frustrating because an elegant type of solution, if it exists, eludes me.  This one in particular seems bothersome.  I have gotten several emails from people about it.  One email, from Ku Chung in Korea, showed me that I had screwed up the solution.  I hope I now have it right.

Here is a simpler version of the puzzle.  It has a different solution from the full puzzle!  Solving this will help you solve the full puzzle.  Anton gives Paul the product and Simon the sum.  Simon and Paul liked this sort of game. Their conversation was the following:

    P: I don't know Anton's numbers.
    S: Hey, now I know.
    P: Then I know them too.
    Math professor observing: "I know Anton's numbers, too!"  Do you?

If you want to see my inelegant solutions, click here.  But if you just want confirmation that its an annoying puzzle, yes, it is.  Or if you want a hint, notice that Paul's inability to produce the numbers right away shows that the number can be factored into two factors in more than one way.  This means that it is not the product of two primes, and also not the cube of a prime (like 8).  The smallest possible such product is P=12.  Both Simon and the math professor know this right away, of course.

Back to Laszlo's puzzles
P. B. Allen, 11/18/2002