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Topic: regular n-gon runners problem
Replies: 12   Last Post: Jul 25, 2013 4:26 AM

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Posts: 12,067
Registered: 7/15/05
regular n-gon runners problem
Posted: Jul 23, 2013 2:33 AM
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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.


If there is an instant where the locations of the n runners are
the vertices of a regular n-gon, then the speeds of the runners,
arranged in ascending order, form an arithmetic sequence.


It's easy to see that the converse holds.


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