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# How many different values can $\lfloor x \rfloor + \lfloor 2x \rfloor + \lfloor 3x \rfloor +\lfloor 4x \rfloor$ take for $0 \leq x \leq 1$?

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How many different values can $$\lfloor x \rfloor + \lfloor 2x \rfloor + \lfloor 3x \rfloor +\lfloor 4x \rfloor$$ take for $$0 \leq x \leq 1?$$

May 4, 2021