The Lonely Runner Conjecture

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.

Try it! (Click the image)

The Lonely Runner

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 🙂

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