# Greek Anthology Book XIV: Metrodorus: 125

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## 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: $125$