Greek Anthology Book XIV: Metrodorus: 120

Arithmetical Epigram of Metrodorus

 * The walnut-tree was loaded with many nuts, but now someone has suddenly stripped it.
 * ''But what does he say?
 * "Parthenopea had from me the fifth part of the nuts,
 * to Philinna fell the eighth part,
 * Aganippe had the fourth,
 * and Orithyia rejoices in the seventh,
 * while Eurynome plucked the sixth part of the nuts.
 * The three Graces divided a hundred and six,
 * and the Muses got nine times nine from me.


 * The remaining seven you will find still attached to the farthest branches."

Solution
Let $n$ be the number of walnuts that were originally on the tree.


 * $\dfrac n 5$ went to Parthenopea


 * $\dfrac n 8$ went to Philinna


 * $\dfrac n 4$ went to Aganippe


 * $\dfrac n 7$ went to Orithyia


 * $\dfrac n 6$ went to Eurynome


 * $106$ went to the three Graces


 * $9 \times 9$ went to the Muses


 * $7$ remain unpicked.

So we have:

So there were $1680$ walnuts on the tree, of which:


 * $336$ went to Parthenopea


 * $210$ went to Philinna


 * $420$ went to Aganippe


 * $240$ went to Orithyia


 * $280$ went to Eurynome

and as we know:


 * $106$ went to the three Graces


 * $81$ went to the Muses

and $7$ remain unpicked.