Nurikabe

Nurikabe is a logic puzzle played on a grid where some cells contain numbers. The player must shade certain cells to create a "river" (connected wall of shaded cells) that flows around numbered "islands." Each number indicates the size of the island (group of connected unshaded cells) it belongs to. The river must form a single connected region, islands cannot touch each other, and no 2x2 square of cells may be entirely shaded. The interplay of island isolation and river connectivity makes Nurikabe one of the most elegant and challenging grid puzzles.

Rules

1. Each numbered cell is part of an island (a group of connected unshaded cells).
2. Each island contains exactly one number, and the number indicates the island's total size in cells.
3. Islands cannot be adjacent to each other horizontally or vertically (they may touch diagonally).
4. All shaded cells must form a single connected group (the "river" or "wall").
5. No 2x2 area of the grid may be entirely shaded (no "pools" in the river).
6. Every cell is either part of an island or part of the river.

Strategies

• Island of 1: A numbered cell with "1" is a complete island by itself. All four orthogonal neighbors must be shaded.
• Unreachable Cells: Cells too far from any numbered cell to be part of any island must be shaded (part of the river).
• Between Islands: If two numbered cells are close together, cells between them that cannot belong to either island (because that would make the island too large or merge two islands) must be shaded.
• Expanding Islands: If an island has only one direction in which it can grow to reach its target size, those cells must be unshaded.
• No Pools (2x2 Rule): If three cells of a 2x2 square are shaded, the fourth must be unshaded. This rule often forces island expansions or prevents shading.
• River Connectivity: If shading a cell would split the river into disconnected parts, that cell must remain unshaded — or conversely, if leaving a cell unshaded would disconnect the river, it must be shaded.

Nurikabe was first published by the Japanese puzzle company Nikoli in their magazine *Puzzle Communication Nikoli* in 1991. The puzzle was contributed by a reader using the pen name "Renin" (れにん). Nikoli has a long tradition of accepting and publishing reader-submitted puzzle designs, and Nurikabe became one of their most successful discoveries.

The name "Nurikabe" comes from Japanese folklore. The nurikabe is a yokai (supernatural creature) — an invisible wall that blocks travelers' paths at night. The connection to the puzzle is the wall of shaded cells that surrounds and separates the numbered islands. This evocative name gives the puzzle a cultural dimension that many solvers appreciate.

Nurikabe has been featured regularly in the World Puzzle Championship since the late 1990s and is considered one of the benchmark puzzle types in competitive puzzling. The interplay of its five constraints — numbered islands, island isolation, river connectivity, the 2x2 rule, and complete coverage — creates puzzles that require deep logical reasoning and careful bookkeeping.

The puzzle has a notable connection to mathematics and computer science. Determining whether a Nurikabe puzzle has a solution is NP-complete, meaning it is computationally hard in general. Despite this theoretical complexity, well-designed Nurikabe puzzles are solvable through human-accessible logic without trial and error. The puzzle appears in Simon Tatham's Portable Puzzle Collection, numerous puzzle apps, and online puzzle platforms. It is widely regarded by puzzle enthusiasts as one of the finest grid puzzles ever created, combining aesthetic beauty with logical depth.