A number of cats killed 999,919 mice between them. How many cats?
Several cats, more than one, killed 999,919 mice between them. Every cat killed the same number of mice, more than one each, and every cat killed more mice than there were cats in total. How many cats were there?
Reveal the answer
991 cats, each killing 1,009 mice (991 × 1,009 = 999,919). The trick is spotting that 999,919 is a semiprime whose only factors besides 1 and itself are 991 and 1,009, and only one of those fits 'more mice per cat than there were cats.' Henry Dudeney set this as puzzle no. 323 in his posthumous 1932 collection, 'Puzzles and Curious Problems.'
— Henry Ernest Dudeney, Puzzles and Curious Problems — 1932, puzzle no. 323 (also no. 251 in the 1968 compilation '536 Puzzles & Curious Problems')
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