WOLFRAM NOTEBOOK

WOLFRAM|DEMONSTRATIONS PROJECT

The Lonely Runner Conjecture

new race

select number of runners

start

There are

runners going around a circular track of unit length. They all start together from the same spot and each one has their own distinct speed. The distance between two runners is the distance around the track between them. A runner is defined as lonely if his distance to any other runner is at least

1/n

The Lonely Runner conjecture states that each runner becomes lonely at some time [1]. The conjecture has been proven for up to seven runners [2].

This Demonstration lets you verify this conjecture. Select a number of runners and start the race. When a runner becomes lonely, his position and his marker on the speed gauge turn red and two red arcs of length

1/n

are displayed fore and aft of his position.

Each new race or renewed selection of the number of runners generates a different set of

random speeds.

You are using a browser not supported by the Wolfram Cloud

Supported browsers include recent versions of Chrome, Edge, Firefox and Safari.

I understand and wish to continue anyway »