Take a group of runners circling a track at unique, constant paces. Answering the question of how many will always end up running alone, no matter their speed, has vexed mathematicians for decades. The original version of this story appeared in Quanta Magazine. Picture a bizarre training exercise: A group of runners starts jogging around a circular track, with each runner maintaining a unique, constant pace. Will every runner end up “lonely,” o... [7116 chars]
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