Tetrominoes

Tetrominoes are geometric shapes formed by joining four unit squares edge to edge. There are exactly 5 distinct free tetrominoes (when rotations and reflections are considered equivalent): the I-piece (straight bar), O-piece (square), T-piece, S-piece (and its mirror Z), and L-piece (and its mirror J). In a tetromino puzzle, the player must arrange a set of these pieces to fill a target shape completely without gaps or overlaps. Unlike the real-time action of Tetris, tetromino puzzles are static — you have all the time you need to think.

Rules

1. You are given a target shape and a set of tetromino pieces.
2. Place all pieces into the target shape.
3. Pieces may be rotated and, depending on the variant, flipped.
4. Pieces must not overlap.
5. The target shape must be completely filled with no gaps.

The 5 Free Tetrominoes

• I: A straight line of 4 squares.
• O: A 2x2 square.
• T: A T-shape (3 in a row with 1 on top of the center).
• S/Z: Two squares on one row, two offset to the side on the next row. S and Z are mirror images.
• L/J: Three in a column with one extending from a corner. L and J are mirror images.

When reflections are counted as different (one-sided tetrominoes), there are 7 distinct pieces.

Strategies

• Place the O-piece First: The square O-piece is inflexible (rotation does not change it), so place it early in a corner or alongside an edge.
• Use I-pieces Along Edges: The straight bar is most useful along the perimeter of the target shape.
• Watch for Parity: Color the target shape like a checkerboard. The T-piece covers 3 of one color and 1 of another, while I, O, S, Z, L, and J each cover 2 of each. Count the color balance to check feasibility.
• Avoid Isolated Gaps: Do not leave holes smaller than 4 cells, as no piece can fill them.
• Work from Constrained Areas: Start filling narrow or irregular parts of the target shape first, then fill open areas with the more flexible pieces.
• Trial and Rotation: Since there are fewer piece types than pentominoes, systematically trying rotations in a small area is practical.

Tetrominoes, as a mathematical concept, were formally defined by Solomon W. Golomb alongside other polyominoes in his 1953 work. However, their fame came not from academic papers but from one of the most influential video games ever made: Tetris.

In 1984, Soviet computer scientist Alexey Pajitnov created Tetris at the Dorodnitsyn Computing Centre of the Soviet Academy of Sciences in Moscow. Pajitnov originally conceived the game using pentominoes (5-square pieces), but found the real-time gameplay too complex. He simplified to tetrominoes, creating the perfect balance of simplicity and challenge. The game's name is a portmanteau of "tetra" (Greek for four) and "tennis," Pajitnov's favorite sport.

Tetris became a worldwide phenomenon after it was bundled with the original Nintendo Game Boy in 1989. The licensing saga of Tetris — involving Soviet bureaucracy, international negotiations, and competing companies — became one of the most dramatic stories in video game history. The game has sold over 500 million copies across all platforms, making it one of the best-selling games of all time.

Static tetromino puzzles (without the real-time falling mechanic) existed before Tetris but were far less popular. After Tetris, the visual language of tetrominoes became universally recognized. Modern tetromino puzzles include filling challenges, covering problems, and educational exercises. The mathematical study of tetrominoes covers tiling theory, computational complexity (determining if a set of tetrominoes can tile a given shape is NP-complete), and combinatorial geometry.