56th Ukrainian National Mathematical Olympiad, Third Round

The numbers $13$, $17$, $19$ may form an integer only if they stand at the numerator position and $1$ stands in the denominator position. Hence, at least one fraction cannot be integer. However, $10$ numbers may occur to be integer: $$\frac{22}{11},\frac{14}{7},\frac{15}{5},\frac{21}{3},\frac{20}{10},\frac{18}{9},\frac{16}{8},\frac{12}{6},\frac{19}{1},\frac{4}{2},\frac{13}{17}$$