The Lonely Runner Conjecture states that if K runners set off at constant different speeds to run laps around a 1 mile circular track then for each runner there is some time when she is at least 1/K miles from all the other runners.
I made a little simulation to help visualise this.
As the wikipedia page shows, the conjecture is proven for K up to 7 (which was shown in 2008), but beyond that we don’t know!
I posted the problem for K = 4 to the Math Riddles subreddit because that place is cool and I like it.
Unfortunately, I posted it slightly wrong by stating “more than” instead of “at least”. This was picked up in a particularly thorough answer 🙂