Epitaph of Diophantus

Classic Problem

 * This tomb holds . Ah, how great a marvel!
 * The tomb tells scientifically the measure of his life.
 * God granted him to be a boy for one-sixth of his life,
 * and adding a twelfth part to this, he clothed his cheeks with down.
 * He lit him the light of wedlock after a seventh part.
 * and five years after his marriage he gave him a son.
 * Alas, late-born wretched child!
 * After attaining the measure of half his father's life, chill Fate took him.
 * After consoling his grief by the study of numbers for four years, ended his life.

Solution
died at the age of $84$.

Let $x$ be the number of years achieved by at his death.

His boyhood took up $\dfrac x 6$ years.

His adolescence took up another $\dfrac x {12}$ years.

After another another $\dfrac x 7$ years he married.

A son was born to him after another $5$ years.

After another $\dfrac x 2$ years, that son died.

(The assumption being made here is the conventional one: that the age of the son at his death is half the age of at the death of  himself, not of his son, which was $4$ years earlier.)

After another $4$ years, himself died.

Thus we have:

Hence :


 * was a boy for $14$ years


 * was a youth for $7$ years


 * married after another $12$ years at the age of $33$


 * had a son born $5$ years later at the age of $38$


 * who died $42$ years later when was $80$


 * and died $4$ years later at the age of $84$.

Also known as
This problem is often referred to as Diophantus's riddle.