# Thread: Problem Of The Week #402 Jan 20th, 2020

1. Here is this week's POTW:

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The set of real numbers $x$ for which

$\dfrac{1}{x-2009}+\dfrac{1}{x-2010}+\dfrac{1}{x-2011}\ge 1$

is the union of intervals of the form $a<x\le b$.

Find the sum of the lengths of these two intervals.

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2.