Learn More
Let A be a set of 2n points in general position on a plane, and suppose n of the points are coloured red while the remaining are coloured blue. An alternating path P of A is a sequence p1, p2,..., p2n of points of A such that p2i is blue and p2i+1 is red. P is simple if it does not intersect itself. We determine the condition under which there exists a(More)
The following problem was posed in the 27th International Mathematics Olympiad (1986): One is given a finite set of points Pn in the plane, each point having integer coordinates. Is it always possible to colour some of the points red and the remaining points white in such a way that, for any straight line L parallel to either one of the coordinate axes, the(More)