Moderately difficult Nurikabe puzzle (solution)

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. Image File history File links A moderately difficult 10x9 Nurikabe logic puzzle. ... Image File history File links A moderately difficult 10x9 Nurikabe logic puzzle. ... Japanese writing Kanji 漢字 Kana 仮名 Hiragana 平仮名 Katakana 片仮名 Uses Furigana 振り仮名 Okurigana 送り仮名 Romaji ローマ字 Hiragana (平仮名 literally smooth kana) are a Japanese syllabary, one of four Japanese writing systems (the others are katakana, kanji and rōmaji). ... Japanese mythology is an extremely complex system of beliefs. ... Nikoli is also a village on the island of Lefkada, see Nikoli, Greece Nikoli (ニコリ) is a Japanese publisher that specializes in puzzles and is also the nickname of the quarterly magazine issued by the company (the full name being Puzzle Communication Nikoli). ...

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 comprise 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 comprised 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. A polyomino is a polyform with the square as its base form. ...

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. A logic puzzle is a puzzle deriving from the mathematics field of deduction. ...

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. Nikoli is also a village on the island of Lefkada, see Nikoli, Greece Nikoli (ニコリ) is a Japanese publisher that specializes in puzzles and is also the nickname of the quarterly magazine issued by the company (the full name being Puzzle Communication Nikoli). ...

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. Go is a strategic, two-player board game originating in ancient China between 2000 BC and 200 BC. Go is a popular game in East Asia. ... Go terms are terms in Go, technical terms likely to be met in books and articles about go in English, and in other languages also. ...

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.)

• Some puzzles will require the location of "unreachables" - cells that cannot be connected to any number, being either too far away from all of them or blocked by other numbers. Such cells must be black. Often, these cells will have only one route of connection to other black cells or will form an elbow whose required white cell (see previous bullet) can only reach one number, allowing further progress.

See also

• Category:Logic puzzles

External links

• Tutorial at Puzzle Japan (the Nikoli website) (Macromedia Flash required); use the tabs at the top of the page to view rules, study solving tips (under "Keys to solution"), and solve beginner and sample problems (Java Applets required)
• Nurikabe at janko.at (German; Java required for sample puzzles)
• Nurikabe is NP-Complete (Adobe Acrobat Reader required)