Mind your S and P's

Appeared in Volume 6/2, May 1993

Here's a logic puzzle, like those posed by Dell's Official Pencil Puzzles and Word Games. I first heard it from Peter Ross (peter@aisb.ed.ac.uk).

The Mr S and Mr P Problem

By David Warren

There are two numbers M and N such that 1 < M & N < 100. Mr S is told their sum S and Mr P is told their product P. The following dialogue takes place:

Mr P: I don't know the numbers.

Mr S: I knew you didn't know them; I don't know them either.

Mr P: Now I know the numbers!

Mr S: Now I know them too!

Question: What are the numbers?

An interesting source of puzzles by the way is Tit Bits magazine, which was published in England from the mid 19th century until the 1960's. In its last days it contained mainly pin-ups and nonsense stories, but early issues printed some interesting puzzles.

Ken Johnson
ken@aiai.ed.ac.uk

The book "Prolog - A logical Approach" by Tony Dodd has the code for a meta-interpreter to solve this type of puzzle.

Carl Lemp
Carl.Lemp@f2206.n124.z1.fidonet.org

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