Nurikabe ぬりかべ

Nurikabe (ぬりかべ) is a shading puzzle played on a square grid with a few numbers scattered across it. You shade cells to build one connected wall, and the cells you leave white form islands. Each number sits in an island of exactly that many cells, every island holds exactly one number, islands never share an edge, and the wall may never contain a solid 2×2 block. A finished grid looks like a map: a winding dark channel with white islands of different sizes between its arms.

Nurikabe is a Nikoli puzzle. The Japanese publisher developed it and named it after the nurikabe, a wall spirit from Japanese folklore that blocks the way of travelers. Nikoli describes it as a puzzle that beginners and experts both enjoy, and its own rules page suggests the classic way in: start from the 1s, whose four neighbors are always wall.

On LogicPuzzles.io there is a new daily 7×7 Nurikabe that is the same for every player, plus unlimited 5×5, 7×7 and 10×10 grids whenever you want another. Every puzzle is checked by two independent solvers to have exactly one solution, and by a deduction grader to be solvable without guessing. Your progress, streak and best times stay in this browser, and it is all free with no account.

Begin with the clues that give themselves away. A 1 is already a complete island, so all four of its neighbors are wall. A blank cell that touches two different numbers would join two islands if it stayed white, so it is wall too, whether the two clues sit two apart in a line or diagonally. Then shade the unreachable cells: a cell that no clue can reach with the cells it has left can never be white.

As islands grow, keep two habits. When an island reaches its full size, surround it with wall at once. When an unfinished island has only one open cell it can grow into, it must grow there, so mark that cell with a dot. Dots record cells you have proved to be white.

The wall has rules of its own. Whenever three cells of a 2×2 square are shaded, the fourth must be white and belong to some island; this pool check often opens up a crowded corner. The wall must also stay in one piece, so a wall segment with only one way out has to extend through it. It helps to count as well: the white cells add up to the sum of the clues, and every other cell is wall.

The most common mistake is an orphan island, a pocket of white cells with no number, sealed off by the wall. Before you close a region, make sure some clue can still reach it. A 2×2 block of shaded cells turns red as soon as it appears, and the Check button points out any shaded cell that really belongs to an island, any dot sitting on a wall cell, and how many wall cells are still to shade.

Nurikabe was developed and named by Nikoli, the Japanese puzzle publisher. The name comes from the nurikabe of Japanese folklore, a spirit that appears as an invisible wall across a traveler’s path; the word itself is usually translated as plaster wall, a fitting picture for the wall of shaded cells that runs between the islands. Outside Japan the puzzle has also been published as Islands in the Stream, a version that calls the wall the stream. In 2004 Markus Holzer, Andreas Klein and Martin Kutrib showed that deciding whether a Nurikabe grid has a solution is NP-complete, which is why good puzzles are built and checked with care so that a single solution can be reached by logic alone. The puzzles here follow Nikoli’s standard rules: numbered islands of the right size, one connected wall and no 2×2 block of wall.