MathDB

265

Part of 1978 All Soviet Union Mathematical Olympiad

Problems(1)

ASU 265 All Soviet Union MO 1978 marking lattice points

Source:

7/11/2019
Given a simple number p>3p>3. Consider the set MM of the pairs (x,y)(x,y) with the integer coordinates in the plane such that 0≤x<p,0≤y<p0 \le x < p, 0 \le y < p. Prove that it is possible to mark pp points of MM such that not a triple of marked points will belong to one line and there will be no parallelogram with the vertices in the marked points.
combinatoricscombinatorial geometrylattice points