Nurikabe
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- This article is about the puzzle. For the Japanese spirit, see Nurikabe (folklore).
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" (which is where Islands in the Stream got its name): 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.
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[edit] 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/)
[edit] 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.
[edit] 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.
- All white cells must eventually be part of exactly one island. If there is a white region that does not contain a number, and there is only one possible way for it to connect to a numbered white region, the sole connecting pathway must be white.
- 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.
[edit] Advanced algorithms
- If there is a square consisting of two adjacent black cells and two adjacent unknown cells, at least one of the two unknown cells must remain white according to the rules. Thus, if one of those two unknown cells (call it 'A') can only be connected to a numbered square by way of the other one (call it 'B'), then B must necessarily be white (and A may or may not be white).
- If an island of size N already has N-1 white cells identified, and there are only two remaining cells to choose from, and those two cells touch at their corners, then the cell between those two that is on the far side of the island must be black.
[edit] See also
[edit] External links
- Nikoli's English page on Nurikabe
- Nurikabe is NP-Complete (Adobe Acrobat Reader required)
