Every cat in a district kills the same number of mice, totalling 1,111,111 mice
In a certain district, every single cat killed exactly the same number of mice as every other cat, and each cat killed more mice than there were cats in the whole district. Between them, the cats killed exactly 1,111,111 mice. How many cats were there?
Reveal the answer
239 cats, each killing 4,649 mice. 1,111,111 factors uniquely as 239 x 4,649 (both prime), and since each cat must kill more mice than there are cats, 239 is the only number of cats that works. From Henry Dudeney's The Canterbury Puzzles (1907).
— Henry Dudeney, The Canterbury Puzzles — 1907, 'The Riddle of St. Edmondsbury'