A farmhand sold fractions of a flock of geese all the way home — none harmed
Jabez sells half the flock plus half a goose to one buyer, then a third of what's left plus a third of a goose to another, then a quarter of the remainder plus three-quarters of a goose to a third, then a fifth of what's left plus a fifth of a goose to a fourth. He arrives home with exactly 19 geese, and not one goose was ever cut up. How many geese did he start with?
Reveal the answer
101 geese. Each sale looks fractional but always lands on a whole number: half of 101 plus half a goose is 51 (leaving 50); a third of 50 plus a third is 17 (leaving 33); a quarter of 33 plus three-quarters is 9 (leaving 24); a fifth of 24 plus a fifth is 5 (leaving 19).
— Henry Dudeney, The Canterbury Puzzles — Puzzle 57, 1907
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