paint in plane
Source: Serbia 2001
April 28, 2008
combinatorics unsolvedcombinatorics
Problem Statement
Determine all positive integers for which there is a coloring of all points in space so that each of the following conditions is satisfied:
(i) Each point is painted in exactly one color.
(ii) Exactly colors are used.
(iii) Each line is painted in at most two different colors.