Nurikabe: Rules and Solving Techniques

Nurikabe is named after a yokai from Japanese folklore, an invisible wall that blocks travellers at night. The puzzle is the same idea in a grid: you paint a wall of dark cells around islands of white ones. It has three rules, and the third does far more work than it first appears to.

The rules

1. Each number is an island. Every numbered cell belongs to exactly one island of connected white cells, and the island's size equals the number. An island contains exactly one number.
2. Islands never touch. Two islands may not be orthogonally adjacent. Diagonal contact is fine.
3. The wall is one piece. Every dark cell must connect to every other dark cell horizontally or vertically.
4. No 2 by 2 wall. The wall may never contain a filled 2 by 2 square anywhere on the grid.

Rules one and two feel like the puzzle. Rules three and four are what you actually solve with.

The opening moves

Three kinds of cell can be marked before any real deduction.

• Between two numbers. Any cell orthogonally adjacent to two different numbered cells must be wall. If it were white it would join two islands, which rule two forbids. On a dense grid this alone marks a dozen cells.
• Diagonal neighbours. If two numbers sit diagonally adjacent, the two cells that complete that square must both be wall for the same reason.
• Unreachable cells. For each empty cell, ask whether any island could extend to it within its number. Count the shortest path in steps. If no island can reach it, it is wall. This is the highest yield technique in the whole puzzle and it usually fills a third of the grid on the first pass.
• Islands of one. A cell marked 1 is a complete island by itself, so all four of its orthogonal neighbours are wall immediately.

Do the unreachable pass before anything clever. Most of a Nurikabe grid is wall, and most of that wall is provable in the first two minutes.

The 2 by 2 rule as a tool

The prohibition on a 2 by 2 wall block is the technique that breaks open the middle game. Whenever three cells of any 2 by 2 square are already wall, the fourth must be white, and therefore belongs to some island. That single forced white cell often reveals which island is growing in that direction, which then forces more wall around it.

Scan for these constantly. After every few wall cells you place, check the squares they complete. It is the difference between grinding and flowing.

Completing islands

• A finished island is surrounded. Once an island has as many white cells as its number, every cell orthogonally touching it is wall. Mark them at once.
• A corridor of one. When an unfinished island has exactly one direction it can grow into, it must grow there. Add the cell and re-evaluate.
• Do not strand the wall. Rule three means the wall must stay one connected piece. If placing a wall cell would seal off a pocket of wall from the rest, that cell must be white instead. This mirrors the isolation rule in Hashi, but inverted: there the islands must connect, here the wall must.

A worked opening

Imagine a grid with a 2 near the top left and a 3 two cells to its right, on the same row, with one empty cell between them. That middle cell touches both numbers, so it is wall. The 2 now has three possible shapes: up, down, or left. The 3 similarly loses its leftward option. If the cell above the middle one is also adjacent to a third number diagonally, it becomes wall too, and suddenly the 2 has one direction left and completes itself. Then all four of its neighbours become wall, and those wall cells start completing 2 by 2 squares elsewhere.

That cascade is the characteristic rhythm of Nurikabe: a slow start, then a run of twenty forced cells, then another pause.

Common mistakes

• Painting wall without checking connectivity. It is easy to build a beautiful wall that is in two pieces. Keep an eye on whether every dark region still has a route to the others.
• Letting islands touch diagonally and panicking. Diagonal contact is legal. Only orthogonal contact is forbidden.
• Skipping the unreachable pass. Players who start with clever deductions work three times as hard as those who start by eliminating what no island can reach.
• Guessing. A properly made Nurikabe has one solution reachable by logic. An impasse is an unapplied technique, usually the 2 by 2 rule.

Where it fits

Nurikabe belongs to the same family as Sudoku, Kakuro and Hashi, published by the Japanese house Nikoli, whose editorial standard is that every puzzle must be solvable by pure deduction with a unique answer. Among them, Nurikabe is the most shape driven: you are reasoning about regions and adjacency rather than digits. The wider history is in the Nikoli puzzle tradition, our combined walkthrough is MyRin Hashi and Nurikabe, and for the number side of the family see Kakuro vs Sudoku.

MyRin includes Nurikabe with 600 levels across easy, medium and hard, alongside 32 other games, free on iOS and Android, with the ebook The Mind Games of Japan included.

FAQ

What are the rules of Nurikabe?

Every numbered cell belongs to one island of white cells whose size equals that number. Each island contains exactly one number. Islands never touch each other horizontally or vertically. All remaining cells form the wall, which must be a single connected group, and the wall must never contain a 2 by 2 filled block.

What is the first thing to do in Nurikabe?

Mark the wall between numbers. Any cell orthogonally adjacent to two different numbered cells must be wall, because islands cannot touch. Then mark every cell that no island can possibly reach, which is usually a large part of the grid.

Why can the wall not have a 2 by 2 block?

It is a rule of the puzzle, and it is also the main solving tool. Whenever three cells of a 2 by 2 square are wall, the fourth must be white, which places island cells you could not otherwise deduce.

Is Nurikabe related to Hashi?

Both come from the Japanese publisher Nikoli and both hinge on connectivity, but they invert it. In Hashi the islands must all be connected to each other. In Nurikabe the islands must stay separate and the wall must be connected.