Diophantus was a famous ancient Greek mathematician. This was carved on his tomb:

Herein lies the remains of Diophantus. God vouchsafed that he should be a boy for the sixth part of his life; when a twelfth was added, his cheeks acquired a beard; He kindled for him the light of marriage after a seventh, and in the fifth year after his marriage He granted him a son. Alas! late-begotten and miserable child, when he had reached the measure of half his father's life, the chill grave took him. After consoling his grief by this science of numbers for four years, he reached the end of his life.

How long did he live?

  • 3
    $\begingroup$ I think it's fine. We've posted classics before. I added the puzzle-history tag. $\endgroup$ Commented Jul 16, 2017 at 9:15
  • $\begingroup$ simple math question disguised in hard to understand text question :) $\endgroup$
    – Oray
    Commented Jul 16, 2017 at 12:39

1 Answer 1


In simpler English, this simply means that for 1/6 of his life, he was a boy. For the next 1/12 he had a beard. After the next 1/7, he married. After 5 years, he had a boy, who lived for half of his life. And 4 years after that, Diophantus died.


Let's assume Diophantus's age at the time of his death is $x$. So, we have:

$$ \frac{x}{6} + \frac{x}{12} + \frac{x}{7} + 5 + \frac{x}{2} + 4= x$$

Solving that, we have

Diophantus lived for 84 years.

  • 2
    $\begingroup$ My initial reaction to the question was of course 42! Therefore you must have missed a factor 2 somewhere :P $\endgroup$
    – oerkelens
    Commented Jul 16, 2017 at 13:40
  • $\begingroup$ @oerkelens So was mine. But, Maths doesn't lie. :) $\endgroup$
    – Sid
    Commented Jul 16, 2017 at 13:49
  • $\begingroup$ @oerkelens Diophantus' son lived for 42 years! $\endgroup$
    – isaacg
    Commented Nov 1, 2023 at 3:58

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