# 168 geometry/coloring/triominoes.p

There is a chess board (of course with 64 squares). You are given 21
"triominoes" of size 3-by-1 (the size of an individual square on a
chess board is 1-by-1). Which square on the chess board can you cut out
so that the 21 triominoes exactly cover the remaining 63 squares? Or is
it impossible?

geometry/coloring/triominoes.s

```||||||||
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---***+*
---...+*
---*+O+*
---*+...
---*+***
```

There is only one way to remove a square, aside from rotations and
reflections. To see that there is at most one way, do this: Label
all the squares of the chessboard with A, B or C in sequence by rows
starting from the top:

```		ABCABCAB
CABCABCA
BCABCABC
ABCABCAB
CABCABCA
BCABCABC
ABCABCAB
CABCABCA
```

Every triomino must cover one A, one B and one C. There is one extra
A square, so an A must be removed. Now label the board again by
rows starting from the bottom:

```		CABCABCA
ABCABCAB
BCABCABC
CABCABCA
ABCABCAB
BCABCABC
CABCABCA
ABCABCAB
```

The square removed must still be an A. The only squares that got
marked with A both times are these:

```		........
........
..A..A..
........
........
..A..A..
........
........
```

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