Zip: Draw One Line Through Every Cell 🧩

The rules

Drag from cell to cell to draw a path. It must:

• be a single unbroken line,
• pass through every cell exactly once, and
• reach the numbered cells in ascending order.

Start at the corners

A corner cell has only two neighbours. Since the path has to enter it and leave it (unless it's an endpoint), both of those connections are forced. That's two free segments before you've thought about anything.

The same logic runs along the edges: any cell where walls or already-used neighbours leave exactly two open sides has both of them forced. Working the boundary inward is almost always faster than starting from the middle.

Dead ends and forced turns

Two eliminations do most of the remaining work.

Don't create an isolated cell. If a move would leave some cell with fewer than two available connections and it isn't an endpoint, that move is wrong. Scan for cells that are about to be orphaned — they veto moves several steps before the mistake becomes visible.

Don't close a loop early. Joining two ends of your own path before it covers every cell is fatal. On a long path this is the mistake people actually make, and it's why the undo button exists.

There's also a parity argument available on rectangular grids: colour the cells like a chessboard, and a path visiting every cell alternates colours. If the two colour counts differ by more than one, no path exists at all — which tells you a great deal about where the endpoints must sit.

About our version

99 levels, growing grids, with walls introduced partway through the curve to prune the search rather than expand it. Drag to draw, drag backwards to erase, unlimited undo. Every level is generated from a known valid path, so a solution always exists.

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

Questions people actually ask

Does the path have to visit every single cell?
Yes. Every cell exactly once, which is what mathematicians call a Hamiltonian path. Missing one cell means the board isn't finished.

Can the path cross itself?
No. Each cell is used once, so the line never crosses or overlaps.

Where should I start?
The corners. A corner has only two neighbours, so both of its connections are forced immediately, and the deductions spread inward from there.

Keep reading

• Domino Fit: Tiling Puzzles and the Parity Trick 🁢 — Cover the board in dominoes with no gaps. There's a colouring argument that rules out half the board's dead ends before you place a single tile.
• 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.
• Logic Puzzle Games: A Guide to the 12 in Go Brain 🧠 — Sudoku, Kakuro, Nonogram, Crowns and eight more. What separates a real deduction puzzle from a guessing game, and which to start with.