2010 AIME I Problem 14

For each positive integer n, let f(n) = \sum_{k = 1}^{100} \lfloor \log_{10} (kn) \rfloor. Find the largest value of n for which f(n) \le 300.

Note: \lfloor x \rfloor is the greatest integer less than or equal to x.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.