Create the above figure with 24 identical dominoes (or prove that this is impossible). They may not overlap.
The above tetrominoes (as seen in Tetris) are sometimes called the O and N tetrominoes. There is a shape that can be built with four O tetrominoes OR with four N tetrominoes. Is there a shape that can be built with an odd number of O tetrominoes OR with an odd number of N tetrominoes? Find such a shape, or prove that it is impossible. You may rotate and flip the tetrominoes, but they may not overlap.