@ Chess Board

If 46 squares are selected at random from a 9*9 chess board and coloured red.Prove that there is atleast one 2*2 block of 4 squares of which atleast 3 are coloured red.

the densest that one can go is having 5 row of red squares, each containing 9 squares each and separated by one row. That makes 45 squares. Now no matter where you put the 46th one, you will be creating 4 cells (2X2) which have 3 red squares each

correct..