Puzzles

The tombstone that does math

An epitaph preserved in the Greek Anthology gives the mathematician Diophantus's life story entirely in fractions: a boyhood, a youth, a bachelorhood, a son born five years into marriage who died four years before his father — all portions of an unstated total. How many years did Diophantus live?

Reveal the answer

84 years. Boyhood was 1/6 of his life (14 years), youth another 1/12 (7 years), then 1/7 more before marriage (12 years); a son arrived 5 years later and died at 42, half his father's final age; Diophantus lived 4 more years after that. It's the oldest widely cited 'age riddle' in mathematical history.

Compiled by Metrodorus; original epigram author unknown, Greek Anthology, Book XIV, Epigram 126 — c. 5th–6th century CE compilation
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