Demochares’ Age Problem: A Classic Puzzle from the Greek Anthology

A Saturday Tradition: Puzzles from Antiquity

Saturday is the perfect time to sit down with a good problem. Continuing our journey through the puzzles of the ancient world, let’s travel to Ancient Greece.

About a thousand years ago, a book called the Greek Anthology came into being — an enormous poetry collection containing thousands of epigrams written by approximately 300 authors, dating back to the 7th century BCE.

Mathematical Problems in the Greek Anthology

Book XIV of the Greek Anthology contains 45 mathematical problems — covering topics like division, cisterns, alloys, and more. Their charm lies in the narrative form of their statements and their elegant simplicity. They feel like something from the early years of school, yet remain close to real, everyday situations.

One of the problems on that list concerns the age of Demochares. Similar problems had appeared even earlier — in Babylonian texts and Egyptian papyri.

Who Was Demochares? The Historical Context

It is unknown whether the problem refers to any real individual, but history does record at least one Demochares. That was the name of an Athenian orator and politician of the 4th century BCE — a nephew of Demosthenes.

The Demochares Age Problem: Statement and Solution

Here is the problem itself:

Demochares lived one-quarter of his life as a boy, one-fifth as a youth, one-third as a man, and when he reached grey old age, he lived thirteen more years. How old was he when he died?

Answer: 60

What Comes Next: The Most Famous Age Problem of Antiquity

Reach 50 reactions on this post and I’ll write about the most famous age puzzle from antiquity — which also, by the way, comes from the Greek Anthology — the problem of Diophantus’ age.