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A **tromino** or **triomino** is a polyomino of size 3, that is, a polygon in the plane made of three equal-sized squares connected edge-to-edge.^{[1]}

When rotations and reflections are not considered to be distinct shapes, there are only two different *free* trominoes: "I" and "L" (the "L" shape is also called "V").

Since both free trominoes have reflection symmetry, they are also the only two *one-sided* trominoes (trominoes with reflections considered distinct). When rotations are also considered distinct, there are six *fixed* trominoes: two I and four L shapes. They can be obtained by rotating the above forms by 90°, 180° and 270°.^{[2]}^{[3]}

Both types of tromino can be dissected into *n*^{2} smaller trominos of the same type, for any integer *n* > 1. That is, they are rep-tiles.^{[4]} Continuing this dissection recursively leads to a tiling of the plane, which in many cases is an aperiodic tiling. In this context, the L-tromino is called a *chair*, and its tiling by recursive subdivision into four smaller L-trominos is called the chair tiling.^{[5]}

Motivated by the mutilated chessboard problem, Solomon W. Golomb used this tiling as the basis for what has become known as Golomb's tromino theorem: if any square is removed from a 2^{n} × 2^{n} chessboard, the remaining board can be completely covered with L-trominoes. To prove this by mathematical induction, partition the board into a quarter-board of size 2^{n−1} × 2^{n−1} that contains the removed square, and a large tromino formed by the other three quarter-boards. The tromino can be recursively dissected into unit trominoes, and a dissection of the quarter-board with one square removed follows by the induction hypothesis.
In contrast, when a chessboard of this size has one square removed, it is not always possible to cover the remaining squares by I-trominoes.^{[6]}

**^**Golomb, Solomon W. (1994).*Polyominoes*(2nd ed.). Princeton, New Jersey: Princeton University Press. ISBN 0-691-02444-8.**^**Weisstein, Eric W. "Triomino".*MathWorld*.**^**Redelmeier, D. Hugh (1981). "Counting polyominoes: yet another attack".*Discrete Mathematics*.**36**: 191–203. doi:10.1016/0012-365X(81)90237-5.**^**Nițică, Viorel (2003), "Rep-tiles revisited",*MASS selecta*, Providence, RI: American Mathematical Society, pp. 205–217, MR 2027179.**^**Robinson, E. Arthur Jr. (1999). "On the table and the chair".*Indagationes Mathematicae*.**10**(4): 581–599. doi:10.1016/S0019-3577(00)87911-2. MR 1820555..**^**Golomb, S. W. (1954). "Checker boards and polyominoes".*American Mathematical Monthly*.**61**: 675–682. doi:10.2307/2307321. MR 0067055..

- Golomb's inductive proof of a tromino theorem at cut-the-knot
- Tromino Puzzle at cut-the-knot
- Interactive Tromino Puzzle at Amherst College