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  1. WLOG put the bugs on a 3×3 checkerboard with 4 black squares & 5 white squares.
    Each bug starts on either a black or white square.

    If each bug moves to an adjacent square, the color of the square that the bug is on will switch.
    In this case, the 4 black square bugs will move to occupy 4 white squares.

    Since there are 5 white squares on our board, there must be at least 1 white square with NO bugs on it.

    We can also come to another conclusion:
    The initial 5 white square bugs will move to occupy 5 black squares.

    Since there are only 4 black squares on our board, there must be at least 1 black square with 2 bugs on it.

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