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From: David Bernier on 10 May 2010 09:11
This is a problem that can be simply stated, which I found here:
< http://garden.irmacs.sfu.ca/?q=op/lonely_runner_conjecture >
(The Open Problem Garden).

There is a unit length circular track with 'k' runners on it.
They all run at constant speeds, which are all distinct.
The conjecture (for 'k' runners) is that for each of the 'k'
runners, there is some time at which he or she is at least
1/k units away from every other runner.

So for k=2, there is always a time where they are 1/2 unit
apart (or separated by 180 degrees if we think of
a perfectly circular track).

From the Open Problem Garden:
<< Recently, the k=7 case was proved by Barajas and Serra [BS]. >>

David Bernier


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