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.