Consider the first quadrant in the Cartesian plane divided into unit squares by horizontal and vertical lines at the positive integers. (1) Place $latex 3$ dots (clones) in the shape of an $latex L$-tromino in the bottom left-most squares, and…

Let $latex R$ be a rectangle with side lengths $latex a$ and $latex b$. Show that if $latex R$ is tiled by rectangles each of which has at least one integer side, then at least one of $latex a$ and…