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 don't know if this is minimum but I have a 24 piece answer for part 2. This size 12 square is divided into 2 by 3 rectangles. The interior of the rectangle denoted by E's has the center of the main square.
AABBAABBAABB
AABBAABBAABB
AABBAABBAABB
BBAACCCDDDAA
BBAACCCDDDAA
BBAAEEECCCAA
AABBEEECCCBB
AABBCCCDDDBB
AABBCCCDDDBB
BBAABBAABBAA
BBAABBAABBAA
BBAABBAABBAA
Part 2 Answer
