Greek Anthology Book XIV: Metrodorus: 137

Arithmetical Epigram of Metrodorus

Let fall a tear as you pass by; for we are those guests of Antiochus whom his house slew when it fell, and God gave us in equal shares this place for a banquet and a tomb.

Four of us from Tegea lie here,

twelve from Messene,

five from Argos,

and half of the banqueters were from Sparta,

and Antiochus himself.

A fifth of the fifth part of those who perished were from Athens,

and do thou, Corinth, weep for Hylas alone.

Solution

Let $n$ be the number of guests who were killed in the accident.

$4$ came from Tegea

$12$ came from Messene

$5$ came from Argos

$\dfrac n 2$ came from Sparta

$1$ was Antiochus

$\dfrac n {5 \times 5}$ came from Athens

$1$ (that is, Hylas) came from Corinth.

We have:

\(\ds n\)

\(=\)

\(\ds 4 + 12 + 5 + \dfrac n 2 + 1 + \dfrac n {25} + 1\)

\(\ds \leadsto \ \ \)

\(\ds 50 n\)

\(=\)

\(\ds 25 n + 2 n + 50 \times 23\)

multiplying through by $50 = \lcm \set {2, 25}$ and simplifying

\(\ds \leadsto \ \ \)

\(\ds \paren {50 - 25 - 2} n\)

\(=\)

\(\ds 50 \times 23\)

\(\ds \leadsto \ \ \)

\(\ds 23 n\)

\(=\)

\(\ds 50 \times 23\)

\(\ds \leadsto \ \ \)

\(\ds n\)

\(=\)

\(\ds 50\)

So there were $50$ guests.

$25$ came from Sparta

$2$ came from Athens

and the numbers of the remainder are specified explicitly.

$\blacksquare$

Source of Name

This entry was named for Metrodorus.

Sources

• 1918: W.R. Paton: The Greek Anthology Book XIV ... (previous) ... (next): Metrodorus' Arithmetical Epigrams: $137$