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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

A region can be tiled by trominoes only if its area is a multiple of 3, since

One of the best-known tiling problems involves tiling a 2^n by 2^n chessboard with one missing square

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

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.
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.
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.
rich
mathematical
structures.