# Nurikabe

Nurikabe, also called Islands in the Stream or Cell Structure, is a type of grid-shading logic puzzle in which solvers must shade in cells in a way that creates 'islands' of certain sizes made up of white squares, while the black 'stream' stays completely connected.

## Background

First published by Nikoli in March of 1991, Nurikabe puzzles were invented by a regular reader who went by the pen name 'Lenin'. While little is known about the author besides their status as a student at the time of their first submission in 1989, they have been attributed with the invention of three prominent Nikoli originals: Slitherlink, Hashiwokakero, and Nurikabe. Nurikabe has appeared in every single issue of the quarterly magazine Nikoli Puzzle Communication since volume 38.

The name Nurikabe (ぬりかべ) comes from the name for an invisible wall in Japanese folklore that would intentionally block roads and footpaths.

## Puzzle Application

Nurikabe puzzles traditionally consist of grids of white cells, where some cells contain a number. The goal is then to shade some of the cells (but never the ones with numbers), so that each number is connected to an 'island' of other white cells with a size equal to that number. There are some additional constraints, however:

• Every 'island' must contain exactly one number. No doubling up with the same number or accidentally creating numberless islands.
• The 'stream' made up of shaded cells must be contiguous and without any 2x2 'pools' forming.
• No two islands can touch, except diagonally.

While some of these constraints may change slightly depending on specific puzzles' rules or grid shape, most will follow these rules consistently.

## Strategy

• A 2-clue where it is known that two adjacent directions (say, south and west) cannot be part of the island, forces the opposite diagonal (in the example, north-east) to be shaded.
• One way to view the shaded cell connectivity rule is this alternative formulation: Consider a group of islands, that are connected diagonally. Only one island in this group may touch the edge of the grid, or else it would split the shaded cells into multiple pieces. Additionally a group of islands cannot "touch itself again" in a loop; doing so would divide the shaded cells into an inside and outside. This means that two clues, both on the edge, must be part of different island groups.
• The no 2x2 shaded cell rule has the implication that any 2x2 area must be reached by some island. This may help with determining, say, that only one clue can reach a certain 2x2 region and therefore you can mark many cells that are part of that island.
• A clue may also be "penned" in a way that it must use all of the cells that it can reach, which can give a substantial amount of information.

## Notable Examples

### Played Straight

• The Lion and the Unicorn (MITMH 2014) (web) - A physical puzzle that was part of the final runaround, this puzzle approached Nurikabe very uniquely. Rather than giving solvers a piece of paper, it presented them with a wooden board (marked with numbers like a regular Nurikabe) and a series of tetrominoes and pentominoes representing water and land. Solvers could then place the blocks on the board to form a completed Nurikabe. It still solved as normal, but had the extra step of finding the pieces that would make the solution possible.
• Invisible Walls (MITMH 2019) (web) - With a title alluding to the meaning of the puzzle's name, this puzzle was primarily just ten normal Nurikabes. No major twists, although realizing that a particular section of the puzzle had to form a valid Braille character did certainly help with deduction.

### Notable Twists

• Chimera (MITMH 2008) (web) - Like the title says, this was a logic puzzle chimera, combining two genres into one. In this case, the given puzzle can be solved both as a Nurikabe and as a Corral puzzle. While they don't interact during solving, the fact that the grid serves a dual purpose is unique.
• 🔔🦇🦇🦇 (MITMH 2022) (web) - While solvers may not know it until reading a particular clue, this Mad Gab-like wordsearch served dual-purpose as a Nurikabe. When all of the clues are solved and their answers in the grid are shaded, the result is a series of islands and a shaded 'stream' that follows normal Nurikabe constrains (no 2x2 blocks, everything interconnected).