MathDB
Given 2k −1 white segments and 2k −1 black ones

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November 3, 2010
pigeonhole principlesymmetrycombinatorics proposedcombinatorics

Problem Statement

On a line are given 2k12k -1 white segments and 2k12k -1 black ones. Assume that each white segment intersects at least kk black segments, and each black segment intersects at least kk white ones. Prove that there are a black segment intersecting all the white ones, and a white segment intersecting all the black ones.