# Removing squares from a chessboard

The squares of a $$2 \times 500$$ chessboard are coloured black and white in the standard alternating pattern. $$k$$ of the black squares are removed from the board at random. What is the minimum value of $$k$$ such that the expected number of pieces the chessboard is divided into by this process is at least $$20$$?

Details and assumptions

The squares removed from the chessboard are not counted as pieces.

A piece of the chessboard is a set of squares joined together along edges. Being connected at corners of squares is not sufficient for two squares to be in the same piece.

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