Question 31
A table tennis tournament is conducted in the following way. In each round, if the number of contestants is odd, one contestant is drawn to proceed automatically to the next round. After that, pairs are drawn from the other contestants. The contestants from each pair compete against each other, and the winner proceeds to the next round. Let $f(n)$ denote the number of rounds in the tournament with $n$ contestants. (For example, $f(5) = 3$.) Determine $f(2013)$ and find the least positive integer $n$ such that $f(n) = f(2013)$.