Split 2016

Relevant wiki: Floor and Ceiling Functions - Problem Solving

Let $x = A + \frac{k}{201}$ where $k,A \in \mathbb{Z}$ and $1\le k \le 200$ .

Then the equation is equivalent to $k+6A=2016$ . Note that $(k,A)=(6,335)$ is a solution. Hence $(k,A)=(6+6m, 335-m)$ , where $1\le 6+6m \le 200$ , are solutions. So $0 \le m \le 32$ and thus there are $\boxed{33}$ solutions.