by Denise Greaves, Ph.D.
Most people are unaware that arithmetical story problems are not an entirely modern phenomenon. We have a number of story problems attributed to a certain Metrodorus, a Greek grammarian who probably lived around 500 CE. These compositions were written in poetic form (in Greek) and have been transmitted to modern times via a larger literary collection known as the Greek Anthology. TheÂ Greek Anthology is a treasure-trove of ancient Greek and Byzantine poems that was compiled in various stages in antiquity and Byzantine times.
The poems contained in the GreekÂ Anthology are epigrams. Originally, an epigram was simply an inscription on a monument or other object that revealed who made it, to whom it was dedicated, who was buried there, or other suchlike information. These epigrams were customarily in a poetic form. To make a long dissertation short, literary epigrams eventually came into vogue. These were poems of the sort that would appear on a monument or gravestone but were not necessarily meant to be engraved in stone.
Metrodorus apparently enjoyed epigrams with number problems. Although most of his “story problem” epigrams are actually not of a funerary nature, these epitaphs seem like a good introduction to these fun gems. The solutions to the following sample of problems are natural numbers and can be solved by algebraic means.
I. How long did Diophantus live?
You may have heard of a Diophantine equation, a type of indeterminate equation. Diophantus was a Greek mathematician who probably lived in the third century CE and wrote a work on algebra known as the Arithmetica as well as a work On Polygonal Numbers. The following problem has been known to appear in modern algebra textbooks.
This grave contains Diophantus. What a great wonder!
For the gravestone cleverly tells the length of his life.
God granted him the fate to be a child for a sixth of his life.
Then, having added a twelfth part, He put down on his cheeks.
After another seventh part, Diophantus grasped the wedding torch.
Five years after his marriage, God granted him a child.
Alas! Late-born wretched youth, who only reached half
the length of his father’s life when cold death took him.
Diophantus, after soothing his grief for four years
by this science of numbers, brought an end to his life.
(Metrodorus, Greek Anthology 14.126)
II. How many guests were at this ill-fated dinner party?
What better way to commemorate the victims of a tragedy than by turning their unfortunate fate into a story problem?
Shed a tear as you pass by, for we here are dinner guests,
whom the house of Antiochus slew when it fell,
and to whom God gave this place as both
a banquet hall and a grave. Four from Tegea lie here;
twelve from Messene; five from Argos.
Half of the dinner guests were from Sparta,
plus Antiochus himself. A fifth of a fifth of those who perished
were Athenians. And you, Corinth, cry for only Hylas.
(Metrodorus, Greek Anthology 14.137)
III. How many children did Philinna bear?
This epigram is a poignant reminder of the high infant mortality rates and low life expectancies in earlier ages (as well as today where medical resources are insufficient).
I am a tomb; I conceal the much-lamented children of Philinna;
I contain, as follows, the fruit of a womb that gave birth in vain.
A fifth of those whom Philinna gave me were young men,
a third were maidens, and three were newly married daughters.
The remaining four descended directly from her womb into the underworld without experiencing sunlight or sound.
(Metrodorus, Greek Anthology 14.125)
IV. How long did Demochares live?
I don’t know anything about the Demochares mentioned here other than how long he lived (assuming I solved the problem correctly).
Demochares lived for a fourth of his entire life
as a child, a fifth as an adolescent,
and a third as an adult. When he reached grizzled old age
he lived his remaining thirteen years on the threshold of death.
(Metrodorus, Greek Anthology 14.127)
I have given my own translation of these epigrams. Moreover, I sincerely hope I haven’t made any typos that
will cause grief and the rending of hair and/or garments. Feel free to give your solutions or other feedback in the comments.