Question 54
Triangle $ABC$ has $AB = 10$, $AC = 17$ and $BC = 21$. Take on the side $BC$ the points $X, Y, Z$ – the feet of the altitude, the bisector and, respectively, the median from $A$. Find the smallest positive integer $n$ with the property: if the side $BC$ is divided into $n$ equal parts by $n - 1$ points, then $X, Y, Z$ are among those points.