TOT 221 1989 Spring S5 integers on regions of planes by N lines
Source:
March 7, 2021
combinatoricscombinatorial geometrylines
Problem Statement
We are given lines ( ) in a plane, no two of which are parallel and no three of which have a point in common. Prove that it is possible to assign, to each region of the plane determined by these lines, a non-zero integer of absolute value not exceeding , such that the sum of the integers o n either side of any of the given lines is equal to . (S . Fomin, Leningrad)