Coloring 6000 points using 10 colors
Source: Iberoamerican Olympiad 2009, problem 6
September 24, 2009
combinatorics proposedcombinatorics
Problem Statement
Six thousand points are marked on a circle, and they are colored using 10 colors in such a way that within every group of 100 consecutive points all the colors are used. Determine the least positive integer with the following property: In every coloring satisfying the condition above, it is possible to find a group of consecutive points in which all the colors are used.