The Perfect Tetris?
I received a set of 21 tetraminos, consisting of 3 copies each of the 7 distinct pieces.
I want to arrange them into a nice rectangle, of area \( 3 \times 4 \times 7 \). For how many rectangle shapes can I fit all of them nicely?
Note: It doesn't matter if there are 2 ways to fill in the rectangle. Rotations / Reflections / Orientation of the rectangle also doesn't matter.