# Diophantus Puzzle - Solution

## The Puzzle:

We know very little about the life of the mathematician Diophantus (often known as the 'father of algebra') except that he came from Alexandria and he lived around the year 250 AD.

However, there remains a riddle that describes the spans of Diophantus's life:

In simpler English it says: Diophantus's youth lasted 1/6 of his life. He had the first beard in the next 1/12 of his life. At the end of the following 1/7 of his life Diophantus got married. Five years from then his son was born. His son lived exactly 1/2 of Diophantus's life. Diophantus died 4 years after the death of his son.

How long did Diophantus live?

However, there remains a riddle that describes the spans of Diophantus's life:

*"This tomb holds Diophantus. Ah, what a marvel! And the tomb tells scientifically the measure of his life. 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."*In simpler English it says: Diophantus's youth lasted 1/6 of his life. He had the first beard in the next 1/12 of his life. At the end of the following 1/7 of his life Diophantus got married. Five years from then his son was born. His son lived exactly 1/2 of Diophantus's life. Diophantus died 4 years after the death of his son.

How long did Diophantus live?

## Our Solution:

Here is an equation to reflect the several ages of Diophantus:

(1/6)x + (1/12)x + (1/7)x + 5 + (1/2)x + 4 = x

Solve that equation and the solution is x = 84 years.

(1/6)x + (1/12)x + (1/7)x + 5 + (1/2)x + 4 = x

Solve that equation and the solution is x = 84 years.