Nurikabe Rules: How to Play, Strategies and Variations

What is Nurikabe?

Nurikabe is a shading puzzle about islands and sea. You start with a grid of empty cells, a few of which contain numbers. Your job is to decide which cells are land (left white) and which are water (shaded black). Each number sits on an island and tells you exactly how many cells that island covers. Everything else is sea, and the sea must flow around the grid as one unbroken body.

The appeal is that the finished grid looks like a little map. Numbered islands of different sizes float in a winding black channel, and every shape is forced by logic alone. There is no arithmetic beyond counting, no language knowledge and no guessing in a well-made puzzle.

If you already enjoy shading puzzles such as Nonograms, Nurikabe will feel familiar at first glance, but the reasoning is quite different. Nonogram clues describe rows and columns. Nurikabe clues describe shapes, and the real difficulty comes from two global rules: the sea has to stay connected, and it can never thicken into a 2×2 block.

A short history

Nurikabe comes from the Japanese puzzle publisher Nikoli, the company that also popularized Sudoku and Kakuro. It first appeared in issue 33 of the magazine Puzzle Communication Nikoli in March 1991, contributed by a setter writing under the pen name "renin".

The name borrows from Japanese folklore. A nurikabe is a yōkai, a supernatural being that takes the form of an invisible wall and blocks the road in front of travelers at night. It is a fitting image for a puzzle in which you build walls of shaded cells. The puzzle has also appeared in English under names such as Cell Structure and Islands in the Stream.

Nikoli has published several books made up entirely of Nurikabe, and the puzzle is a regular in logic puzzle collections worldwide. Computer scientists have also shown that solving Nurikabe in general is NP-complete, which is a formal way of saying that large grids can become genuinely hard. The Wikipedia article on Nurikabe covers that background in more detail.

The core rules

Nurikabe has six rules. Every standard puzzle follows all of them, and each one gives you a different kind of deduction.

1. 1Numbers are islandsEvery numbered cell is part of a white island, and the number equals the total number of cells in that island, counting the numbered cell itself.
2. 2One number per islandEach island contains exactly one numbered cell. An island with no number, or with two numbers, is not allowed.
3. 3Islands never touchTwo different islands may not share an edge. They can meet at a corner (diagonally), but never side by side.
4. 4One connected seaAll shaded cells must form a single group, connected horizontally or vertically. No part of the sea may be cut off.
5. 5No 2×2 poolsThe sea may never contain a 2×2 square of shaded cells anywhere in the grid.
6. 6Orthogonal connections onlyBoth islands and sea connect through shared edges. Diagonal contact never joins two cells into the same group.

The no-pool rule is the one beginners forget, and it is also the most useful. Any time three cells of a 2×2 square are shaded, the fourth must be white, and that single fact solves a surprising number of cells.

A solved example

Here is a small 5×5 puzzle with five clues and its unique solution. Try it yourself before looking at the right-hand grid.

Notice how it unfolds. The 1 in the top right is already a complete island, so the cells below it and to its left are sea. The 2 at the left edge and the 2 in the middle are only two cells apart, so the cell between them must be sea, otherwise the two islands would touch. From there the no-pool rule and the need to keep the sea connected force the rest, including the top-left 3 running along the top row and the bottom 3 running to the right.

How to play: a step-by-step method

Every Nurikabe grid is different, but this routine will get you started on any of them and keeps you from staring at an empty board.

1. Finish the 1s first. A 1 is a complete island on its own. Shade every cell that shares an edge with it.
2. Separate neighboring clues. When two numbered cells sit one cell apart in a row or column, the cell between them must be sea. When two clues touch diagonally, both cells that meet both of them must be sea.
3. Mark unreachable cells as sea. If no island is large enough to stretch to a cell, that cell can only be water. Corners and the space between large gaps are the usual candidates.
4. Grow islands that have only one exit. If an unfinished island is walled in on all sides but one, it must expand through that gap. Keep extending until it is complete, then seal it with sea.
5. Check every 2×2 square. Wherever three cells of a square are shaded, the fourth must belong to an island. Ask which island can reach it.
6. Keep the sea flowing. If a shaded area is in danger of being cut off, the cells that link it to the rest of the sea must also be shaded. Repeat these checks until the grid is full.

Strategies experienced solvers use

Once the basic steps feel natural, these techniques will carry you through medium and hard grids. Most of them are ways of combining two rules at once.

Hard puzzles usually hinge on a short chain: an unreachable cell becomes sea, that sea threatens a 2×2 pool, the pool forces an island cell, and the island's shape then reaches back and settles another region. If you are stuck, look for the place where two of these rules overlap.

Variations and related puzzles

Standard Nurikabe is by far the most common form, but you will meet a few relatives and twists.

• Question-mark clues. Some puzzles place a ? in a cell to show that it belongs to an island without revealing the size. It still counts as that island's one clue.
• Mochikoro. A Nikoli relative in which the unshaded areas must be rectangles and the white regions link together only through their corners. The no-pool rule still applies.
• LITS. Another Nikoli shading puzzle where you place a tetromino in every outlined region. It shares Nurikabe's connected shaded area and its ban on 2×2 blocks.
• Hexagonal grids. Variants on hexagonal tilings exist, which change how many neighbors each cell has and make the connection rules feel very different.
• Loop and bridge cousins. If you like Nurikabe's connectivity logic, Hashi asks you to connect islands with bridges, while Slitherlink and Masyu ask you to draw a single loop.

Common mistakes

The most common error by far is leaving a 2×2 pool in the sea. It is easy to shade cells one at a time without noticing that four of them have closed into a square, so check the neighborhood each time you shade.

Next is letting islands touch. Two islands that meet along an edge have merged into one island with two numbers, which breaks the rules. Remember that diagonal contact is fine: islands meeting only at a corner are still separate.

Third, solvers forget that every white cell needs a number. You cannot leave a stray white cell in the middle of the sea just to avoid a pool. If a cell must be white, some numbered island has to grow far enough to include it.

Finally, miscounting island size trips people up. The number includes the numbered cell itself, so a 3 means the clue plus two more cells, not three more.

How difficulty scales

Beginner grids are usually 5×5 to 7×7 with plenty of small clues. Lots of 1s and 2s mean that the separating and reachability steps solve most of the board, and the pool rule mops up the rest.

Medium and hard puzzles, often 10×10 and up, use fewer and larger clues. A big island has many possible shapes, so you lean more heavily on the global rules: the sea's connectivity and the no-pool constraint. Expect longer chains of reasoning where a deduction on one side of the grid settles a region on the other.

If you enjoy that global style of logic, try Star Battle next, which uses a similar mix of local and whole-grid constraints with stars instead of shading.

Frequently asked questions