UNSOLVED PROBLEMS |

In Number Theory, Logic, and Cryptography |

Lonely Runner Conjecture |

Suppose there are k runners, all lined up at the start of a circular running track of length 1. They all start running at constant, but different, speeds.
The Lonely Runner conjecture states that for each runner, there will come a time when he or she will be a distance of at least 1/k along the track from every other runner. The conjecture has been proved for small values of k (<=7). The problem is to prove or disprove the conjecture for the general case, or for cases where k > 7.
For further information, please see: [1] http://stathletics.tumblr.com/post/21662762724/the-lonely-runner-conjecture [2] http://en.wikipedia.org/wiki/Lonely_runner_conjecture [3] https://rjlipton.wordpress.com/2012/01/28/the-lonely-runner-conjecture/
You can check for contributions to this problem on the solutions page. ——————————–- This web site developed and maintained by Tim S Roberts Email: timro21@gmail.com |