Consider the circle C of length 1 and a circular arc A of length $\ell \in (0,1)$. It is shown that there exists $k=k(\ell )\in \mathbb{N}$, and a schedule for k runners along the circle with k constant but distinct positive speeds so that at any time $t\ge 0$, at least one of the k runners is not in A.

On the other hand, we show the following. Assume that k runners $1,2,\dots ,k$, with constant rationally independent (thus distinct) speeds ${\xi }_1,{\xi }_2,\dots ,{\xi }_k$, run clockwise along a circle of length 1, starting from arbitrary points. For every circular arc $A\subset C$ and for every $T>0$, there exists $t>T$ such that all runners are in A at time t.

Several other problems of a similar nature are investigated.

考虑圆Ç长度为1的和圆弧甲长度的$\ell \in （0，\mathrm{1个}）$。显示存在$ķ=ķ（\ell ）\in \mathbb{ñ}$，以及针对k个跑步者的时间表，其中k个跑步者的k个常数不变，但正向速度不同，因此可以随时$Ť\ge 0$中，至少一个ķ参赛者是未在甲。

另一方面，我们显示以下内容。假设有k个跑步者$\mathrm{1个}，2，\dots ，ķ$，具有恒定的理性独立（因此截然不同）的速度 ${\xi }_{\mathrm{1个}}，{\xi }_2，\dots ，{\xi }_{ķ}$，从任意点开始沿长度为1的圆顺时针运行。对于每个圆弧$\mathrm{一种}\subset C$ 而对于每个 $Ť>0$， 那里存在 $Ť>Ť$使得所有跑步者在时间t处在A中。

研究了类似性质的其他几个问题。