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.
Today i will introduce colouring proofs. For this i will give the classic example.
Let a chessboard be given. The two black corners are cut off. Is it possible to completely cover the board with domino bricks.
No. A domino brick on the board always covers one black and one white tile. Since there are more white tiles than black tiles, it is impossible to completely cover the board with dominoes.