Today i will post another easy coloring proof:
Can you completely cover a 10×10 chess board with 4×1 bricks.
We colour the board, so that we have a 5×5 chessboard in which each tile consists of 4 of the 10×10 board tiles.
Then every 4×1 Brick touches 2 black and 2 white tiles. (The 10×10 board tiles) but their are more tiles of one colour than the other. This is a contradiction.