Simplifying expression composed of floor functions

Question

We are given expression: $$\left\lfloor \frac{x+2}{6}\right\rfloor -\left\lfloor \frac{x+3}{6}\right\rfloor +\left\lfloor \frac{x+4}{6}\right\rfloor$$ Simplify it so that it contains minimal number of floor functions. How to do that? Even Mathematica cannot do it. Although we know it can be done as can be seen here.