Math Puzzle: A Tetris paradox

In Tetris, players arrange seven different shaped pieces to fill a rectangular space efficiently. It is impossible to arrange all seven pieces into a rectangle if you have exactly one of each shape. However, discarding one piece allows for such an arrangement. The piece that must be discarded is the T-shaped piece.

Visualize a checkerboard pattern on the rectangle, where each square is the same size as the pieces. Each Tetris piece, whether rotated or not, will cover two white squares and two black squares on the checkerboard. The T-shaped piece is the only one that will cover three squares of one color and one square of the other color. This creates an imbalance that cannot be corrected by the other pieces.

To form a rectangle with the remaining six pieces, a 3 x 8 or 4 x 6 configuration works. Discard the T-shaped piece and arrange the other pieces accordingly. This puzzle demonstrates a neat mathematical principle involving parity and the arrangement of shapes within a rectangular space.