The Lonely Runner Conjecture
The Lonely Runner Conjecture imagines a finite number of runners, each with a distinct (constant) speed, running around a circular track of unit length. The conjecture states that for each runner there will be some time at which that runner will be lonely, that is, separated from each of the other runners by a distance of at least 1k, where k is the number of runners. As of 2008, this conjecture has been proven for up to seven runners.
Choose the number of runners using the slider and click the button to start or stop the run. The runners all start together (happy face), but it appears that eventually each of them will become lonely (sad face) at some point. When this happens for the first time, the face turns gray and stays that way.
Number of runners:
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