Tetris is played with quadrominoes; figures made up of four squares stacked edge to edge. The goal is to fill completely rows of the well with the pieces that fall down into the well. In Tetris one may move the pieces right or left and rotate them 90, 180, or 270 degrees. If an entire row is filled with pieces, then that row disappears.
Problem 1. Determine all possible quadrominoes. Do not distinguish two quadrominoes if one can be obtained from the other by a rotation. The quadrominoes you get are the Tetris pieces.
Problem 2. How many quadrominoes are there if you do not distinguish between two pieces for which one can be turned into the other by a flip or a rotation?
Problem 3. How many different arrangements of the Tetris pieces can be made by rotating the seven Tetris pieces?
Problem 4. For which Tetris pieces can you fill the well, with no gaps, using only copies of the one piece, and thus making all of the pieces dissapear? Consider the well to be 12 squares wide for this question. If a piece can fill the well, what is the smallest number of rows that can be completely packed with copies of the piece?