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# Floor and ceiling

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

Dec 18, 2020

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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?