218. Someone bought 30 birds for 30 coins, among these birds, for every 3 sparrows, 1 coin was paid, for every 2 doves, also 1 coin, and finally, for each pigeon - 2 coins. How many birds of each kind were there?

## Problem of John of Palermo.
218. We have the system: $x+y+z=30 ; \frac{1}{3} x+\frac{1}{2} y+2 z=30$, where $x$ is the number of sparrows, $y$ is the number of magpies, and $z$ is the number of pigeons. Eliminating $z$: $10 x+9 y=180$ and $y=20-\frac{10}{9} x$. For $x$ the only value is 9. Consequently, $y=10$ and $z=11$.