Question 160
There are $n$ white and $n$ black balls placed randomly on the circumference of a circle. Starting from a certain white ball, number all white balls in a clockwise direction by $1, 2, \dots, n$. Likewise, number all black balls by $1, 2, \dots, n$ in an anti-clockwise direction starting from a certain black ball. Prove that there exist consecutive $n$ balls whose numbering forms the set $\{1, 2, \dots, n\}$.