We are given N lines (N>1 ) 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 N , such that the sum of the integers o n either side of any of the given lines is equal to 0 . (S . Fomin, Leningrad) combinatoricscombinatorial geometrylines