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Combinatorics: Covering a 4x4 Chessboard with Dominoes
How many ways are there to cover a 4x4 Chessboard with Dominoes?
2x2 is trivial.
There are just 2 ways: horizontal or vertical.
To solve 4x4 we proceed systematically, putting a horizontal or vertical domino in the first available space (from the top left).
The diagram shows half of them. The other half are the diagonally mirrored versions of these, with the first domino placed vertically.
The numbers in the grids represent how many ways there are to complete the grid from the given start. (There are 3 ways to fill a 2x3 rectangle.)
For a general formula, and the very much larger numbers of ways for larger squares, see:
A004003
in the OEIS
or
Domino Tiling
in Wikipedia.
2x2 is trivial.