Problem

Source: 25th Olympic Revenge

Tags: combinatorics, Chessboard



positive real C is nvengeful if it is possible to color the cells of an n×n chessboard such that: i) There is an equal number of cells of each color. ii) In each row or column, at least Cn cells have the same color. a) Show that 34 is nvengeful for infinitely many values of n. b) Show that it does not exist n such that 45 is nvengeful.