Spencer's Single Lonely Runner Conjecture

Let $V=\{v_1,\dots,v_n\}$ be an $n$-set of pairwise distinct real speeds, and let $\|x\|$ denote the distance from $x$ to the nearest integer. Single Lonely Runner Conjecture. For every $n\in\mathbb{N}$ and every such $V$, there exist $i\in[n]$ and $t\in\mathbb{R}$ such that

$$\min_{j\neq i}\|t(v_j-v_i)\|\geq\frac{1}{n}.$$

This weakening, attributed to Joel Spencer, asks only for one runner to become lonely rather than requiring the assertion for every runner. It is presented as an open problem in the survey.