1999 OIM Problems/Problem 3
Problem
Let there be 
different points, 
, on a straight line of the plane (
). We consider the circles of diameter 
(
) and we color each circle with one of 
given colors. We call this configuration 
-th.
For each positive integer , find all for which every 
th is verified to contain two externally tangent circles of the same color.
NOTE: To avoid ambiguity, points that belong to more than one circle do not have a color.
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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