Answer to the Problem of the Week

for the week of January 10, 2000

Diophantus' Age Problem
Diophantus, the Greek mathematician known as the "Father of Algebra", supposedly had the following inscribed on his tombstone:
"Diophantus passed 1/6th of his life in childhood, 1/12th in youth, and 1/7th more as a bachelor.
Five years after his marriage, there was born a son who died four years before his father, at half his father's age."

How old was Diophantus when he died?

 

  In 1987, I wrote a similar problem, highlighting the significant events of my life.
To see this problem, click here: Mr. P's Algebra Problem

Click here to see Diophantus' actual epitaph


Solution:

Diophantus died at age 84.

You could solve the problem using algebra by letting x = the age of Diophantus at his death.
However, there is an easier way to solve the problem. The only number divisible by 6, 12, and 7, and also a number in the human lifespan is 84.
So, he spent 14 years in childhood, seven in youth, and 12 as a bachelor.
He married at 33, and five years afterward, at age 38, a son was born who later died at age 42, when Diophantus was 80.
Four years after that, Diophantus himself died at 84, twice the age to which his son lived.

Correctly solved by:

1. Tom Marino Winchester, VA
2. Steven R. Muller Clearbrook, VA
3. Court Pifer Winchester, VA
4. Chip Crawford Winchester, VA