The following is a combinatorics problem that I need help with. I have no idea how to go about it. Any help is deeply appreciated.
All points in a 100x100 array are coloured in one of four colours red, green, blue and yellow, in such a way that there are 25 points of each colour in any row and in any column. Prove that there are two rows and two columns such that their four intersection points are all different colours.