# International Mathematics Competition for University Students 2021

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IMC 2021
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## IMC2021: Day 1, Problem 3

Problem 3. We say that a positive real number $\displaystyle d$ is good if there exists an infinite sequence $\displaystyle a_1,a_2,a_3,\ldots \in (0,d)$ such that for each $\displaystyle n$, the points $\displaystyle a_1,\dots,a_n$ partition the interval $\displaystyle [0,d]$ into segments of length at most $\displaystyle 1/n$ each. Find

$\displaystyle \sup\Big\{d\ \big|\ d \text{ is good}\Big\}.$