## Dudeney's Catching the Mice puzzle

### D. Joyce Clark University

#### A classic puzzle

Here's one of H. E. Dudeney's many interesting puzzles.

Catching the mice. A cat is in the center of a circle of mice. Twelve of the mice are black, one is white.

"Play fair!" said the mice. "You know the rules of the game."

"Yes, I know the rules," said the cat. "I've got to go round the circle, in the direction you are looking, and eat every thirteenth mouse, but I must keep the white mouse for a tid-bit at the finish. Thirteen is an unlucky number, but I will do my best to oblige you."

"Hurry up, then!" shouted the mice.

"Give a fellow time to think," said the cat. "I don't know which of you to start at. I must figure it out."

While the cat was working out the puzzle, he fell asleep, and, the spell being thus broken, the mice returned home in safety. At which mouse should the cat have started the count in order that the white mouse should be the last eaten?

When the reader has solved that little puzzle, here is a second one for him. What is the smallest number that the cat can count round and round the circle, if he must start at the white mouse (calling that "one" in the count) and still eat the white mouse last of all?

And as a third puzzle try to discover what is the smallest number that the cat can count round and round if she must start at the white mouse (calling that "one") and make the white mouse the third eaten?

Don't peek here until you've played with the problem for a while.

Sept 2003
D. Joyce
Department of Mathematics and Computer Science
Clark University
This file is located at http://aleph0.clarku.edu/~djoyce/puzzles/mice.html