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Researchers Advance 'Lonely Runner' Problem for Up to Ten Runners

4/18/2026

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Summary

Story summary

Researchers Matthieu Rosenfeld and Tanupat Trakulthongchai advanced the proof of the "lonely runner" problem for eight, nine, and ten runners on a circular track with unique speeds.
The work, rooted in a conjecture dating to the 1960s, connects to number theory and graph theory and renews interest in the problem.
Matthias Beck of San Francisco State University notes that proving the conjecture for more runners becomes exponentially harder.

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Story summary

Researchers Matthieu Rosenfeld and Tanupat Trakulthongchai advanced the proof of the "lonely runner" problem for eight, nine, and ten runners on a circular track with unique speeds.
The work, rooted in a conjecture dating to the 1960s, connects to number theory and graph theory and renews interest in the problem.
Matthias Beck of San Francisco State University notes that proving the conjecture for more runners becomes exponentially harder.