Greek Anthology Book XIV: Metrodorus: 116

Arithmetical Epigram of Metrodorus

Mother, why dost thou pursue me with blows on account of the walnuts? Pretty girls divided them all among themselves.

For Melission took two-sevenths of them from me,

and Titane took the twelfth.

Playful Astyoche and Philinna have the sixth and third.

Thetis seized and carried off twenty,

and Thisbe twelve,

and look there at Glauce smiling sweetly with eleven in her hand.

This one nut is all that is left to me.

Solution

Let $n$ be the total number of walnuts.

$\dfrac {2 n} 7$ were taken by Melission.

$\dfrac n {12}$ were taken by Titane.

$\dfrac n 6$ were taken by Astyoche.

$\dfrac n 3$ were taken by Philinna.

$20$ were taken by Thetis.

$12$ were taken by Thisbe.

$11$ were taken by Glauce.

$1$ remains to the poor narrator.

Hence:

\(\ds n\)

\(=\)

\(\ds \dfrac {2 n} 7 + \dfrac n {12} + \dfrac n 6 + \dfrac n 3 + 20 + 12 + 11 + 1\)

\(\ds \leadsto \ \ \)

\(\ds 84 n\)

\(=\)

\(\ds 24 n + 7 n + 14 n + 28 n + 84 \times 44\)

multiplying through by $84 = 7 \times 12$ and simplifying

\(\ds \leadsto \ \ \)

\(\ds \paren {84 - 24 - 7 - 14 - 28} n\)

\(=\)

\(\ds 84 \times 44\)

\(\ds \leadsto \ \ \)

\(\ds 11 n\)

\(=\)

\(\ds 84 \times 44\)

\(\ds \leadsto \ \ \)

\(\ds n\)

\(=\)

\(\ds \dfrac {84 \times 44} {11}\)

\(\ds \)

\(=\)

\(\ds 336\)

So the narrator started with $336$ walnuts, of which:

$96$ were taken by Melission

$28$ were taken by Titane

$56$ were taken by Astyoche

$112$ were taken by Philinna

and as we know:

$20$ were taken by Thetis

$12$ were taken by Thisbe

$11$ were taken by Glauce

and $1$ remains to the narrator.

$\blacksquare$

Source of Name

This entry was named for Metrodorus.

Sources

• 1918: W.R. Paton: The Greek Anthology Book XIV ... (previous) ... (next): Metrodorus' Arithmetical Epigrams: $116$