The game is played on a square board divided into 20 rows and 20 columns, for a total of 400 squares. There are a total of 84 game tiles, organized into 21 shapes in each of four colors: blue, yellow, red, and green. The 21 shapes are based on free polyominoes of from one to five squares (one monomino, one domino, two trominoes/triominoes, five tetrominoes, and 12 pentominoes).
In recreational mathematics, a polyomino is a polyform with the square as its base form. It is a connected shape formed as the union of one or more identical squares in distinct locations on the plane, taken from the regular square tiling, such that every square can be connected to every other square through a sequence of shared edges (i.e., shapes connected only through shared corners of squares are not permitted). Polyominoes with from 1 to 6 squares are called respectively monominoes, dominoes, trominoes (or triominoes), tetrominoes, pentominoes and hexominoes. Polyominoes have been used in popular puzzles since at least 1907, and the enumeration of pentominoes is dated to antiquity. Many results with the pieces of 1 to 6 squares were first published in Fairy Chess Review between the years 1937 to 1957, under the name of "dissection problems". The name polyomino was invented by Solomon W. Golomb in 1953 and they were popularized by Martin Gardner.
I've only thrown the tiles, the whole lot of them, fancy names and all, at the Professor once for blocking my most stellar move.