Question 2
Find the total number of different integer values taken by
$$f(x)=\lfloor x\rfloor+\lfloor2x\rfloor+\left\lfloor\frac{5x}{3}\right\rfloor+\lfloor3x\rfloor+\lfloor4x\rfloor$$
for real $x$ with $0\le x\le100$. Here $\lfloor t\rfloor$ is the greatest integer not exceeding $t$.
$$f(x)=\lfloor x\rfloor+\lfloor2x\rfloor+\left\lfloor\frac{5x}{3}\right\rfloor+\lfloor3x\rfloor+\lfloor4x\rfloor$$
for real $x$ with $0\le x\le100$. Here $\lfloor t\rfloor$ is the greatest integer not exceeding $t$.