Nurikabe Puzzles
Shade the sea around the numbered islands. Each number is an island of exactly that many unshaded cells, islands never touch side by side, the whole sea stays in one piece — and no 2×2 block may be entirely sea. Tap once for sea, again to mark island. Every grid has one answer, reachable without a single guess.
Named by Nikoli after the nurikabe of Japanese folklore — an invisible wall that blocks travellers on night roads.
Related Practice
What Is A Nurikabe Puzzle?
Nurikabe hands you a grid with a few numbers on it and asks you to paint the sea. Every number marks an island — a group of exactly that many unshaded cells — and everything that is not island is shaded sea. Nikoli published it in 1991, and the name is borrowed from a spirit of Japanese folklore: an invisible wall that appears across the road at night and will not let travellers pass. A fair name for the black wall you are building around each island.
The Four Rules, And What Each One Gives You
| Rule | What it demands | What you deduce from it |
|---|---|---|
| Islands match their number | One number per island, exactly that many cells | A finished island is fenced by sea on every side. |
| Islands stay apart | No two islands touch side by side | Any cell between two numbers is sea at once. |
| One sea | All shaded cells connected | A pocket of sea with one way out must take it. |
| No 2×2 sea | Every 2×2 square keeps some land | Three shaded cells in a square settle the fourth as island. |
The Move That Fills Most Of The Grid
Ask of any empty cell: which number could reach this? An island of k can stretch at most k − 1 steps from its number, never through sea, and never into a cell beside a different island. Most cells on the board are reachable by only one number, and a cell reachable by none is sea, immediately. Solvers who work reach first and rules second finish these grids in half the time, because reach is the rule that decides the middle of the board where nothing else applies.
The count nobody uses, and should. The sea always holds exactly the grid size minus the sum of the numbers — on a 7×7 with numbers adding to 18, exactly 31 cells of sea. Keeping that running total tells you when the sea is finished, and the moment it is, everything still empty is island. The board's counter shows both totals for exactly this reason.
How These Grids Are Made — And Why The Sea Is Grown As A Tree
Every grid here is generated, and the construction is what guarantees the shape rules rather than checking them afterwards. The sea is grown as a tree: starting from one cell, it only ever adds a cell touching exactly one existing sea cell. A set of cells with no cycles cannot contain a 2×2 block — a 2×2 block is a cycle — and a tree is connected by definition. So rules three and four hold before a single number is placed, and the islands are simply whatever the sea leaves behind.
The numbers are then placed one per island, and the grid is kept only if two separate checks both pass: an exhaustive count finds exactly one arrangement that fits, and a solver restricted to the reasoning on this page finishes the whole grid without guessing. Where the number sits inside its island turns out to matter enormously — the same layout can be ambiguous with the number in the middle and airtight with it on a corner — so several placements are tried before a layout is given up on.
Nurikabe Puzzles Frequently Asked Questions
What is a nurikabe puzzle?
A logic puzzle where you shade a sea around numbered islands. Each number marks an island of exactly that many unshaded cells, islands never touch side by side, the sea is one connected piece, and no 2×2 block is all sea. Nikoli named it after the nurikabe of Japanese folklore — an invisible wall that blocks travellers at night.
What are the rules of nurikabe?
Four. Every island holds exactly one number and exactly that many cells. Islands never touch side by side — corners are fine. All shaded cells form one connected sea. And no 2×2 area is ever entirely shaded.
What is the first move in a nurikabe puzzle?
Fence every 1: an island of one is already complete, so all four neighbours are sea. Then shade any cell sitting between two different numbers — one cell cannot belong to two islands.
Why can no 2×2 block be all sea?
It is a rule in its own right, and a productive one: whenever three cells of a 2×2 square are shaded, the fourth must be island — before you know which number owns it. It also forces the sea into the corridors that give nurikabe its look.
How do you know a cell must be sea?
The strongest everyday reason is reach: if no number could stretch that far, the cell can only be sea. Counting decides cells too — the sea always holds exactly the grid size minus the sum of the numbers, so when one side is full, everything left is the other.
Is nurikabe related to minesweeper or nonogram?
It shares the shaded-grid family with nonogram, but the reasoning differs: a nonogram is decided line by line, nurikabe by shape — what stays connected, what gets walled off, how far a number can reach.
Does every puzzle here have one answer?
Yes, and it is checked twice rather than claimed: an exhaustive count confirms exactly one arrangement fits, and a separate solver that never guesses must finish the grid unaided.
What does nurikabe mean?
A nurikabe is a creature from Japanese folklore — an invisible wall that appears in front of travellers at night and blocks the road, its name meaning roughly "painted wall". The puzzle is named after it because the sea you paint is exactly that: one continuous wall winding between the islands, blocking every route from one to another.