Tiling Puzzles

Dominoes, colourings and counting

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Colouring arguments: each domino covers one black and one white square.
• Domino tilings of a 2 × n strip are counted by the Fibonacci numbers.
• Any 2ⁿ × 2ⁿ board minus one square tiles with L-trominoes (proof by induction).

Steps

1. The mutilated chessboard
2. Counting domino tilings
3. A longer strip
4. L-shaped trominoes
5. A different cut
6. Three rows high