Combinatorics on intersection of lines
Source: St. Petersburg MO 2000, 9th grade, P4; 10th grade P3
April 22, 2023
analytic geometrygeometrycombinatoricscombinatorial geometry
Problem Statement
On a Cartesian plane 101 planes are drawn and all points of intersection are labeled. Is it possible, that for every line, 50 of the points have positive coordinates and 50 of the points have negative coordinates[I]Proposed by S. Ivanov