Suppose that n a’s and n b’s are distributed around the outside of a circle. Use mathemati...

Suppose that n a’s and n b’s are distributed around the outside of a circle. Use mathematical induction to prove that for all integers n ≥ 1, given any such arrangement, it is possible to find a starting point so that if one travels around the circle in a clockwise direction, the number of a’s one has passed is never less than the number of b’s one has passed. For example, in the diagram shown below, one could start at the a with an asterisk.