Greek Anthology Book XIV: 1. - Problem

Problem

 * Polycrates Speaks


 * Blessed, Helliconian scion of the Muses, answer my question: How many in thy house are engaged in the contest for wisdom performing excellently?


 *  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 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:

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