Tromino

A tromino is a polyomino of order 3, formed by three equal squares connected edge-to-edge. The name combines tri- meaning three with the -omino suffix used for polyominoes, and it is widely used in tiling theory and recreational mathematics.

There are two free trominoes, distinguished up to rotation and reflection: the straight tromino (also called the I-tromino), which consists of three squares in a straight line, and the L-tromino, which forms an L shape. If orientation is counted as distinct, there are six fixed trominoes: two orientations of the I-tromino (horizontal and vertical) and four orientations of the L-tromino.

A region can be tiled by trominoes only if its area is a multiple of 3, since each tile covers three unit squares. Simple examples include tiling a 1x3 rectangle with one I-tromino, or a 2x3 rectangle with two I-trominoes. More complex regions may require a mixture of tromino types and careful arrangement.

One of the best-known tiling problems involves tiling a 2^n by 2^n chessboard with one missing square using L-trominoes. This problem has a classic divide-and-conquer solution: place a central L-tromino to cover the three quadrants not containing the missing square, then recurse on the four quadrants. The problem is a staple in discussions of inductive tiling methods and recursive algorithms.

Trominoes appear in tiling theory, combinatorics, and puzzle design, illustrating how simple building blocks can create rich mathematical structures.