How many different values can $\lfloor x \rfloor + \lfloor 2x \rfloor + \lfloor 3x \rfloor +\lfloor 4x \rfloor$ take for $0 \leq x \leq 1$?
If x=0 what is the answer?
If x=1 what is the answer?
If x= just a tiny bit less than 1, what is the answer?
Try x=1/4, x=1/3, x=1/2, x=2/3,
What do you have so far?
Please let guest asker answer this.