AMC 10 Step by Step
2016 AMC 10BProblem 25P21-25~10 minPrint

Let f(x)=k=210(kxkx)f(x)=\sum_{k=2}^{10}(\lfloor kx \rfloor -k \lfloor x \rfloor) , where r\lfloor r \rfloor denotes the greatest integer less than or equal to rr . How many distinct values does f(x)f(x) assume for x0x \ge 0 ?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.