Domino Fit: Tiling Puzzles and the Parity Trick 🁢

The rules

Place 2×1 dominoes on the board — horizontally or vertically — until every open cell is covered. No overlaps, no gaps, no domino hanging off the edge or over a blocked cell.

The parity trick

Colour the board like a chessboard, alternating light and dark. Every domino, wherever you put it, covers exactly one light cell and one dark cell. It cannot do otherwise.

That gives you a free test: if the board doesn't have equal numbers of light and dark cells, it cannot be tiled at all. The classic demonstration is a chessboard with two opposite corners removed — both corners are the same colour, so the remaining 62 squares split 30/32 and no arrangement of 31 dominoes can cover it. No searching required; the colouring settles it.

In play, you use it locally. When your placements have carved the remaining space into a region with unequal counts, that region is dead — undo back to the branch point rather than fiddling with it. Learning to see that imbalance is what makes the late levels tractable.

Forced cells

The other technique is simpler: find any open cell with exactly one open neighbour. Its domino is forced. Place it, and often a new cell becomes forced next to it — these chains run surprisingly long, especially into the corners and dead-end arms of a shaped board.

Between forced chains and parity checks, most levels resolve without any real trial and error.

About our version

99 levels with boards that start rectangular and grow holes and awkward arms as you climb. Drag along two cells to place a domino, tap to remove, unlimited undo. Every board is generated from a valid tiling, so a solution always exists.

It runs in your browser, works offline once loaded, needs no account, and costs nothing.

Questions people actually ask

What is the parity trick in domino tiling?
Colour the board like a chessboard. Every domino covers one light and one dark cell, so a region with unequal light and dark counts can never be tiled. It rules out dead ends instantly.

Can dominoes be rotated?
Yes — every domino can be placed horizontally or vertically. That's the only transformation there is.

Is every board solvable?
Yes. Each level is generated from a complete valid tiling and then presented to you, so a solution is guaranteed to exist.

Keep reading

• Patch: Shikaku, the Rectangle-Cutting Puzzle ▭ — Divide the grid into rectangles, each containing one number equal to its area. Primes are your best friends here — and they tell you exactly where to start.
• Zip: Draw One Line Through Every Cell 🧩 — One line, every cell, numbers in order. A Hamiltonian path puzzle that looks like doodling and plays like deduction.
• Block Fit: No Gravity, No Rotation, No Excuses 🧱 — Three pieces at a time on an 8×8 board. You can't rotate them, which means bad boards are always something you did three moves ago.