# Greek Anthology Book XIV: Metrodorus: 125

## Arithmetical Epigram of Metrodorus

I am a tomb and I cover the lamented children of Philinna, containing fruit of her vainly-travailing womb such as I describe.
Philinna gave me my fifth portion of young men,
my third of maidens,
and three newly married daughters;
the other four descended to Hades from her womb without participating at all in the sunlight and in speech.

## Solution

Let $n$ be the number of children of Philinna.

$\dfrac n 5$ were young men
$\dfrac n 3$ were maidens
$3$ were newly married daughters
$4$ were still-born.

We have:

 $\ds n$ $=$ $\ds \dfrac n 5 + \dfrac n 3 + 3 + 4$ $\ds \leadsto \ \$ $\ds 15 n$ $=$ $\ds 3 n + 5 n + 15 \times 7$ multiplying through by $15 = \lcm \set {5, 3}$ and simplifying $\ds \leadsto \ \$ $\ds \paren {15 - 3 - 5} n$ $=$ $\ds 15 \times 7$ $\ds \leadsto \ \$ $\ds 7 n$ $=$ $\ds 15 \times 7$ $\ds \leadsto \ \$ $\ds n$ $=$ $\ds 15$

So Philinna had $15$ children, of which:

$3$ were young men
$5$ were maidens

and as we know:

$3$ were newly married daughters
$4$ were still-born.

$\blacksquare$

## Source of Name

This entry was named for Metrodorus.