🎉🏆🎉
You tiled the whole board!
The Puzzle
A domino covers exactly 2 squares side by side.
A normal 8×8 chessboard has 64 squares, and can be tiled with 32 dominoes.
But what if you remove 2 squares? Can you always tile the remaining 62 squares with 31 dominoes?
Sometimes yes, sometimes no! The answer depends on which squares you remove.
A normal 8×8 chessboard has 64 squares, and can be tiled with 32 dominoes.
But what if you remove 2 squares? Can you always tile the remaining 62 squares with 31 dominoes?
Sometimes yes, sometimes no! The answer depends on which squares you remove.
How to Play
- Choose a challenge or pick Free Play
- Click 2 squares to remove them
- Hover to preview your piece
- Click to place it
- Press R to rotate
- Try to fill every remaining square!
Start with dominoes — the coloring argument is about them. Then try other shapes: does the same-color impossibility still hold? What changes?
The Secret
Try the Opposite Corners challenge first. Struggle with it for a while.
Then click "Show Chessboard Coloring" to reveal the hidden pattern...
The key question: what color are the squares you removed?
Then click "Show Chessboard Coloring" to reveal the hidden pattern...
The key question: what color are the squares you removed?
The domino rule
Every domino, whether horizontal or vertical, always covers exactly one dark and one light square.
So 31 dominoes need exactly 31 dark and 31 light squares.
If you remove two squares of the same color, you get 32 vs 30 — impossible!
If you remove two squares of different colors, you get 31 vs 31 — always possible!
So 31 dominoes need exactly 31 dark and 31 light squares.
If you remove two squares of the same color, you get 32 vs 30 — impossible!
If you remove two squares of different colors, you get 31 vs 31 — always possible!