Greek Anthology Book XIV: Metrodorus: 138

Arithmetical Epigram of Metrodorus

 * Nicarete, playing with five companions of her own age,
 * gave a third of the nuts she had to Cleis,
 * the quarter to Sappho,
 * and the fifth to Aristodice,
 * the twentieth and again the twelfth to Theano,
 * and the twenty-fourth to Philinnis.


 * Fifty nuts were left for herself.

Solution
Let $n$ be the number of nuts in total.


 * $\dfrac n 3$ went to Cleis


 * $\dfrac n 4$ went to Sappho


 * $\dfrac n 5$ went to Aristodice


 * $\dfrac n {20} + \dfrac n {12}$ went to Theano


 * $\dfrac n {24}$ went to Philinnis


 * $50$ stayed with Nicarete.

We have:

So there were $1200$ nuts.


 * $400$ went to Cleis


 * $300$ went to Sappho


 * $240$ went to Aristodice


 * $60 + 100 = 160$ went to Theano


 * $50$ went to Philinnis

and we know that Nicarete kept $50$.