🎉🏆🎉
You tiled the whole board!
The Puzzle
An L-tromino is a piece shaped like an "L" that covers exactly 3 squares.
The challenge: take a 2n × 2n grid, remove one square, and tile the rest using only L-trominoes.
The amazing fact: it's always possible, no matter which square you remove!
The challenge: take a 2n × 2n grid, remove one square, and tile the rest using only L-trominoes.
The amazing fact: it's always possible, no matter which square you remove!
Why the numbers work
A 2n × 2n grid has 4n squares.
Remove 1, and you get 4n − 1 squares left.
Since each L-tromino covers 3 squares, you need (4n − 1) ÷ 3 pieces.
4x4: 16 − 1 = 15 = 5 × 3 ✔
8x8: 64 − 1 = 63 = 21 × 3 ✔
Remove 1, and you get 4n − 1 squares left.
Since each L-tromino covers 3 squares, you need (4n − 1) ÷ 3 pieces.
4x4: 16 − 1 = 15 = 5 × 3 ✔
8x8: 64 − 1 = 63 = 21 × 3 ✔
How to Play
- Pick a grid size
- Click a square to remove it
- Hover to preview your piece
- Click to place it
- Press R to rotate
- Fill every remaining square!
Start with L-trominoes — they always work! Then try other shapes and see what happens. Can you still tile the board? Why or why not?
The Big Idea
The secret is recursion — the same trick repeated at smaller and smaller scales (like fractals!).
Split the board into 4 quarters. One quarter has the missing square. Place one L-tromino at the center covering one cell from each of the other three quarters.
Now each quarter has exactly one "missing" cell — and each is a smaller version of the same puzzle!
Try the Guided Discovery Mode to see this step by step, or click "Watch the Recursive Solution" to see the algorithm in action.
Split the board into 4 quarters. One quarter has the missing square. Place one L-tromino at the center covering one cell from each of the other three quarters.
Now each quarter has exactly one "missing" cell — and each is a smaller version of the same puzzle!
Try the Guided Discovery Mode to see this step by step, or click "Watch the Recursive Solution" to see the algorithm in action.