Greek Anthology Book XIV: Metrodorus: 116

Arithmetical Epigram of Metrodorus

 * Mother, why dost thou pursue me with blows on account of the walnuts? Pretty girls divided them all among themselves.


 * For Melission took two-sevenths of them from me,
 * and Titane took the twelfth.
 * Playful Astyoche and Philinna have the sixth and third.
 * Thetis seized and carried off twenty,
 * and Thisbe twelve,
 * and look there at Glauce smiling sweetly with eleven in her hand.


 * This one nut is all that is left to me.

Solution
Let $n$ be the total number of walnuts.


 * $\dfrac {2 n} 7$ were taken by Melission.


 * $\dfrac n {12}$ were taken by Titane.


 * $\dfrac n 6$ were taken by Astyoche.


 * $\dfrac n 3$ were taken by Philinna.


 * $20$ were taken by Thetis.


 * $12$ were taken by Thisbe.


 * $11$ were taken by Glauce.


 * $1$ remains to the poor narrator.

Hence:

So the narrator started with $336$ walnuts, of which:


 * $96$ were taken by Melission


 * $28$ were taken by Titane


 * $56$ were taken by Astyoche


 * $112$ were taken by Philinna

and as we know:


 * $20$ were taken by Thetis


 * $12$ were taken by Thisbe


 * $11$ were taken by Glauce

and $1$ remains to the poor narrator.