There is a chess board (of course with 64 squares).

geometry/coloring/triominoes

Problem

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?

Show solution

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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..
                ........
                ........