quasi
Posts:
10,317
Registered:
7/15/05


regular ngon runners problem
Posted:
Jul 23, 2013 2:33 AM


Suppose n runners, n >= 3, start at the same time and place on a circular track, and proceed to run counterclockwise along the track (forever), each at a distinct positive constant speed.
Conjecture:
If there is an instant where the locations of the n runners are the vertices of a regular ngon, then the speeds of the runners, arranged in ascending order, form an arithmetic sequence.
Remark:
It's easy to see that the converse holds.
quasi

