1.49 long segment [ILL 1977]
Source:
January 11, 2011
combinatorics proposedcombinatorics
Problem Statement
Several segments, which we shall call white, are given, and the sum of their lengths is . Several other segments, which we shall call black, are given, and the sum of their lengths is . Prove that every such system of segments can be distributed on the segment that is long in the following way: Segments of the same colour are disjoint, and segments of different colours are either disjoint or one is inside the other. Prove that there exists a system that cannot be distributed in that way on the segment that is long.