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 Algebra problem

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How many different values can $\lfloor x \rfloor + \lfloor 2x \rfloor + \lfloor 3x \rfloor +\lfloor 4x \rfloor + \lfloor 5x \rfloor +  \lfloor 6x \rfloor$ take for $0 \leq x \leq 1$?

 

How many different values can    ⌊x⌋+⌊2x⌋+⌊3x⌋+⌊4x⌋+⌊5x⌋+⌊6x⌋   take for   0≤x≤1 ?

 Nov 7, 2021
edited by Alan  Nov 7, 2021

1+0 Answers

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If n is a positive integer, and 0≤x≤1 then ⌊nx⌋ can take take the values 0, 1, 2, ... n   i.e it can take n+1 values.

 

This should help you to answer the question.

 Nov 7, 2021

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