IMC 2021 · Problem 3

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

$$\sup\big\{d \mid d \text{ is good}\big\}.$$