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