Greek Anthology Book XIV: 1. - Problem

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. That is the number of interpreters of the Muses I gather round me.

Solution
It is apparent 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:

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:
 * $14 + 7 + 4 + 3 = 28$

Historical Note
In 's translation of, this is attributed to.