Greek Anthology Book XIV: 1. - Problem
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Problem
- Polycrates Speaks
- Blessed Pythagoras, Helliconian scion of the Muses, answer my question: How many in thy house are engaged in the contest for wisdom performing excellently?
- Pythagoras Answers
- I will tell thee the, Polycrates.
- Half of them are occupied with belles lettres;
- a quarter apply themselves to studying immortal nature;
- a seventh are all intent on silence and the eternal discourse of their hearts.
- There are also three women,
- and above the rest is Theano.
- I will tell thee the, Polycrates.
- That is the number of interpreters of the Muses I gather round me.
Solution
It is apparent from what follows that Theano is not actually counted with the others.
Let $n$ be the number of students.
Then:
- $\dfrac n 2$ are occupied with belles lettres
- $\dfrac n 4$ apply themselves to studying immortal nature
- $\dfrac n 7$ are all intent on silence and the eternal discourse of their hearts
- $3$ are women.
Thus:
\(\ds n\) | \(=\) | \(\ds \dfrac n 2 + \dfrac n 4 + \dfrac n 7 + 3\) | ||||||||||||
\(\ds \leadsto \ \ \) | \(\ds 28 n\) | \(=\) | \(\ds 14 n + 7 n + 4 n + 84\) | multiplying through by $28$ | ||||||||||
\(\ds \leadsto \ \ \) | \(\ds 3 n\) | \(=\) | \(\ds 84\) | gathering terms | ||||||||||
\(\ds \leadsto \ \ \) | \(\ds n\) | \(=\) | \(\ds 28\) | dividing both sides by $3$ |
Thus of those not women:
- $14$ are occupied with belles lettres
- $7$ apply themselves to studying immortal nature
- $4$ are all intent on silence and the eternal discourse of their hearts
and it is seen that:
- $14 + 7 + 4 + 3 = 28$
$\blacksquare$
Historical Note
In W.R. Paton's translation of The Greek Anthology Book XIV, this is attributed to Socrates.
Sources
- 1918: W.R. Paton: The Greek Anthology Book XIV ... (next): $1$. -- Socrates: Problem