It is easy to dissect a square into an odd number of congruent pieces such that the center of the square is completely inside one of the pieces. It is harder to do so with an even number of pieces.

(1) Find the smallest even number of pieces for which this is possible.

(2) Find the smallest even number of rectangular pieces for which this is possible.

I got part 1 down to 6 with this arrangement:

+--+--+--+

| | /|

| | / |

+ +--+ +

| / | |

|/ | |

+--+--+--+

| / |

| / |

+--+--+--+