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.

Sources

• 1918: W.R. Paton: The Greek Anthology Book XIV ... (previous) ... (next): Metrodorus' Arithmetical Epigrams: $125$