How to solve Nurikabe

What is Nurikabe?

Nurikabe is a logic puzzle first published by Nikoli in March 1991. The name comes from a yokai in Japanese folklore — an invisible wall that blocks travelers on dark roads. In the puzzle, you receive an N×N grid with a few numbered cells scattered across it. Everything else is blank. Your job: determine which blank cells are “sea” (black) and which belong to numbered “islands” (white).

The trick is that the sea and the islands have opposing connectivity rules. All sea cells must link up into one mass, while each island must be its own separate group. That tension is the heart of Nurikabe. It also goes by “Islands in the Stream” (Conceptis) and “Cell Structure” (Wikipedia), though most solvers just call it Nurikabe.

The four rules

1. Island size matches the clue: Each numbered cell is part of a white island. The number tells you how many cells that island contains (including the numbered cell itself). A cell marked “3” belongs to a three-cell island.
2. One clue per island: Every island has exactly one numbered cell. Two numbers can never share the same island. This also means different islands can't touch orthogonally — if they did, they'd merge into one island with two clues.
3. Connected sea: All black (sea) cells must form a single orthogonally connected group. You should be able to travel from any sea cell to any other by stepping through adjacent sea cells.
4. No 2×2 pools: No 2×2 block of cells may be entirely black. This prevents the sea from forming wide squares and forces it to flow in channels.

Worked example: 5×5 grid

Imagine a 5×5 grid with three clue cells: a “1” in the top-left corner, a “3” near the center, and a “2” in the bottom-right area.

Step 1 — Isolate the 1. The cell numbered 1 is a complete island all by itself. Mark all four orthogonal neighbors as sea. That's four forced sea cells immediately.

Step 2 — Find unreachable cells. Look at cells far from any clue. If a cell is too distant from every numbered cell to possibly belong to any island (considering the island's maximum size), it must be sea. On a 5×5 grid this usually identifies another two or three cells.

Step 3 — Check for 2×2 pools. With several sea cells placed, check every 2×2 region. If three corners of any 2×2 block are sea, the fourth corner has to be white.

Step 4 — Expand islands. The “3” needs two more white cells. If it can only expand in one direction without touching another island or creating a disconnected sea, those cells are forced. Same logic for the “2.” Fill them in, mark remaining blank cells as sea, and verify the sea is connected. Done.

Solving techniques

1. Island isolation

Cells numbered 1 are complete islands. Every orthogonal neighbor must be sea. This is the most basic technique and usually your starting point. On easy grids, island isolation combined with unreachable-cell logic solves the whole puzzle.

2. Touching fields

Two different numbered cells that are diagonally adjacent share one or two cells between them that adjoin both. Since islands can't touch orthogonally, the cells occupying the shared edge must be sea. More generally, any cell that would connect two different islands if it were white has to be sea instead.

3. Neighbor cells and the L-shape elbow

Consider a cell numbered 2. Its island consists of itself and one adjacent cell. If the numbered cell sits in a corner or along an edge, only two or three expansion directions exist. The cells diagonal to the expansion paths can be resolved. For instance, if a “2” can only expand right or down, the cell diagonally down-right from the numbered cell must be sea — either expansion direction puts the second island cell adjacent to it but on the other side from the number, so it can't belong to this island (one cell too many) and can't belong to another island (that island would touch this one).

4. 2×2 avoidance

Whenever three cells of a 2×2 block are sea, the fourth must be white. This comes up constantly in medium and harder puzzles. Scan the grid for L-shaped clusters of sea cells and force the missing corner to white. Sometimes this creates a chain: forcing one white cell completes a nearby island, whose capping creates new sea cells, which form another L-shape, forcing another white cell.

5. Connectivity forcing

The sea must stay connected. If marking a cell as white would split the sea into two or more separate groups, that cell must be sea. The reverse applies too: if marking a cell as sea would isolate a group of sea cells from the rest, something is wrong upstream. On hard and expert grids, this is often the technique that breaks open a stalled puzzle.

6. Unreachable fields

Every white cell must belong to some island. If a cell is too far from every numbered clue to be part of any island — meaning the Manhattan distance exceeds the remaining capacity of every island it could theoretically reach — it must be sea. On larger grids, this technique eliminates many cells early and narrows the search space considerably.

7. Unique expansion

When an island still needs to grow and can only expand in one direction (all other neighbors are sea or belong to other islands), that expansion cell is forced white. This often triggers a cascade: the newly white cell may complete another island (cap it with sea) or create a 2×2 constraint, leading to further deductions.

Difficulty levels

Nurikabe on ThePuzzleLabs comes in five levels that differ by grid size and the techniques needed:

• Easy (5×5): Island isolation and unreachable cells solve most of the grid. Good for getting comfortable with the four rules.
• Medium (7×7): The 2×2 avoidance rule and neighbor reasoning become necessary. Islands start interacting with each other more.
• Hard (10×10): Connectivity forcing enters as a core technique. You need to think globally about the sea's shape, not just locally.
• Expert (12×12): Multi-step chains. Connectivity and expansion deductions interleave across 144 cells.
• Einstein (15×15): 225 cells worth of deep inference. Solvable by logic alone, but the chains are long and the interactions between islands are dense.

Nurikabe vs other puzzles

Hitori is the closest relative. Both come from Nikoli, both use a three-state cell cycle (unmarked, black, white), and both involve reasoning about connectivity. The key difference: in Hitori, black cells can't touch and white cells must connect. In Nurikabe, black cells must connect and white islands must stay separate. The constraints are essentially mirrored.

Minesweeper shares the grid-deduction feel — numbered clues constrain what can be placed in adjacent cells. The reasoning shares a similar flavor even though the specific rules are different. Slitherlink, another Nikoli creation, exercises similar spatial reasoning about connectivity (the loop must be connected), but through edge-drawing instead of cell-shading.

Common mistakes

Forgetting that islands can't touch each other. This is implicit in the rules (one clue per island), but easy to miss in practice. If two clue cells are close together, the gap between their islands must be filled with sea.

Ignoring the 2×2 rule while focused on islands. It's natural to concentrate on growing islands and marking unreachable cells as sea. But the sea has constraints too. After a batch of sea placements, always scan for 2×2 pools. Catching them early prevents dead ends.

Not checking sea connectivity until the end. On larger grids, a sea placement early in the solve can create a disconnection that only becomes visible much later. Periodically verify that all placed sea cells can still reach each other (potentially through unresolved cells). The validator in ThePuzzleLabs highlights disconnected sea groups to help with this.

Frequently asked questions