Henry Ernest Dudeney/Puzzles and Curious Problems/323 - Cats and Mice/Solution

Puzzles and Curious Problems by Henry Ernest Dudeney: $323$

Cats and Mice

A number of cats (more than one) killed between them $999 \, 919$ mice, and every cat killed an equal number of mice (more than one).

Each cat killed more mice than there were cats.

How many cats were there?

Solution

$991$ cats.

Proof

$999 \, 919$ is a semiprime whose proper divisors are $991$ and $1009$.

$\blacksquare$

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Solutions: $323$. -- Cats and Mice
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $251$. Cats and Mice