Games - Nurikabe

	Games - Nurikabe

:This article is about the puzzle. For the Japanese spirit, see Nurikabe (Japanese mythology).

Nurikabe is a binary determination puzzle. The name is Japanese, in which it is written in hiragana (ぬりかべ); a "nurikabe" in Japanese folklore is an invisible wall that blocks roads and upon which delays in foot travel are blamed. Nurikabe was apparently invented and named by Nikoli
; other names (and attempts at localization) for the puzzle include Cell Structure and Islands in the Stream.

The puzzle is played on a grid, typically rectangular with no standard size. Some cells of the grid start containing numbers. The goal is to determine whether each of the cells of the grid is "black" or "white" (Islands in the Stream calls these "water" and "land" respectively). The black cells form "the nurikabe" (Islands in the Stream calls it "the stream"): they must all be orthogonally contiguous (form a single polyomino), number-free, and contain no 2x2 or larger solid rectangles (Islands in the Stream calls such illegal blocks "pools"). The white cells form "islands" (Islands in the Stream calls these "islands", curiously enough): each number n must be part of an n-omino composed only of white cells. All white cells must belong to exactly one island; islands must have exactly one numbered cell. Solvers will typically shade in cells they have deduced to be black and dot (non-numbered) cells deduced to be white.

Like most any other pure-logic puzzle, a unique solution is expected; a grid containing random numbers is highly unlikely to provide a uniquely solvable Nurikabe puzzle.

Although the rules are slightly more complicated than many other puzzles of this sort, they quickly become instinctual, and the depth of the logic and aesthetics of its construction can quickly be appreciated. Even the most challenging of Nurikabe can be tackled by the inexperienced if given sufficient time; experts can solve the same puzzles in a tenth of that time or less, having learned various tactics to employ for numerous situations.
History
Nurikabe was first developed by "reenin (れーにん)," whose pen name is the Japanese pronunciation of "Lenin" and whose autonym can be read as such, in the 33rd issue of (Puzzle Communication) Nikoli
at March 1991. It soon created a sensation, and has appeared in all issues of that publication from the 38th to the present.

As of 2005, seven books consisting entirely of Nurikabe puzzles have been published by Nikoli.

(This paragraph mainly depends on "Nikoli complete works of interesting-puzzles(ニコリオモロパズル大全集)." http://www.nikoli.co.jp/storage/addition/omopadaizen/)
Solution methods
No blind guessing should be required to solve a Nurikabe puzzle. Rather, a series of simple procedures and rules can be developed and followed, assuming the solver is sufficiently observant to find where to apply them.

The greatest mistake made by beginning solvers is to concentrate solely on determining black or white and not the other; most Nurikabe puzzles require going back and forth. Marking white cells may force other cells to be black lest a section of black be isolated, and vice versa. (Those familiar with Go
can think of undetermined cells next to various regions as "liberties" and apply "atari" logic to determine how they must grow.) Oddly, the easiest rule to forget is the most basic one: all cells must be either black or white, so if it can be proved a cell isn't one, it must be the other.

Here are some basic algorithms:

Since two islands may only touch at corners, cells between two partial islands (numbers and adjacent white cells that don't total their numbers yet) must be black. This is often how to start a Nurikabe'' puzzle, by marking cells adjacent to two or more numbers as black.

Once an island is "complete" - that is, it has all the white cells its number requires - all cells that share a side with it must be black. Obviously, any cells marked with '1' at the outset are complete islands unto themselves, and can be isolated with black at the beginning.

Whenever three black cells form an "elbow" - an L-shape - the cell in the bend (diagonally in from the corner of the L) must be white. (The alternative is a "pool", for lack of a better term.)

All black cells must eventually be connected. If there is a black region with only one possible way to connect to the rest of the board, the sole connecting pathway must be black.

[ Visit the complete Wikipedia entry for Nurikabe ]

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