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If a square must be white and only two islands can connect to it and have no unidentified cells left after connecting, then if the islands connect at a 90-degree angle (ex: One island can connect to the top side and the other to the right side) the cell inside the angle (The one touching the top-left
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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
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If there is a square consisting of two black cells and two 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
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The puzzle is played on a typically rectangular grid of cells, some of which contain numbers. Cells are initially of unknown color, but can only be black or white. Two same-color cells are considered "connected" if they are adjacent vertically or horizontally, but not diagonally. Connected white
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Undetermined cells adjacent to a straight row (or a straight column) of black cells can be tested for being black, because if they are black it will form two elbows, and there will be two adjacent white cells which need to be reachable from the islands. If they can not be fulfilled within the
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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
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Corollary: there cannot be a continuous path, using either vertical, horizontal or diagonal steps, of white cells from one cell lying on the edge of the board to a different cell like that, that encloses some black cells inside, because otherwise, the black cells won't be
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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
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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
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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.)
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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 a way to start a
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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.
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was first developed by "renin (γγΌγ«γ)," whose pen name is the
Japanese pronunciation of "Lenin" and whose autonym can be read as such, in the 33rd issue of (Puzzle Communication)
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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
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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.
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Each numbered cell belongs to a white area, the number indicates how many cells belong to the white area. Some white areas may not include a numbered cell.
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The greatest mistake made by beginning solvers is to concentrate solely on determining black or white and not the other; most
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at March 1991. It soon created a sensation, and has appeared in all issues of that publication from the 38th to the present.
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an elbow whose required white cell (see previous bullet) can only reach one number, allowing further progress.
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Human solvers typically dot the non-numbered cells they've determined to be certain to belong to an island.
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Either one can be ignored, giving a total of three variants. As it turns out, they are all NP-complete.
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An example of the third advanced strategy. The cell diagonally between the two islands has to be black.
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that blocks roads and delays foot travel. Nurikabe was apparently invented and named by the publisher
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corner of the white square in the previous example) must be black to avoid connecting the 2 islands.
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There must be only one sea, which is not allowed to contain "pools", i.e. 2Γ2 areas of black cells.
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https://web.archive.org/web/20060707011243/http://www.nikoli.co.jp/storage/addition/omopadaizen/
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This paragraph mainly depends on "Nikoli complete works of interesting-puzzles(γγ³γͺ γͺγ’γγγΊγ«ε€§ε
¨ι)."
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A Nurikabe puzzle being solved by a human. Dots represent the cells that are known to be white.
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and employ similar solution methods. The binary determination puzzle
Atsumari is similar to
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Each numbered cell is an island cell, the number in it is the number of cells in that island.
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NW Conference of the CSCC, 2004. Also presented at Reed
Mathematics Colloquium, 2004.
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The challenge is to paint each cell black or white, subject to the following rules:
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can think of undetermined cells next to various regions as "liberties" and apply "
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377:"On The NP-Completeness of The NURIKABE Pencil Puzzle and Variants Thereof"
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constraints, it means the cell that was probed for blackness must be white.
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On The NP-Completeness of The NURIKABE Pencil Puzzle and
Variants Thereof
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Proceedings of the 3rd
International Conference on Fun with Algorithms
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to solve
Nurikabe, even when the involved numbers are 1 and 2 only.
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puzzle, by marking cells adjacent to two or more numbers as black.
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cells form "islands", while connected black cells form the "sea".
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but based upon a hexagonal tiling rather than a square tiling.
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This article is about the puzzle. For the
Japanese spirit, see
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The black cell must not cover an area of 2x2 cells or larger.
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must necessarily be white (and A may or may not be white).
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Holzer, Markus; Klein, Andreas; Kutrib, Martin (2004).
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Each island must contain exactly one numbered cell.
417:Markus Holzer, Andreas Klein and Martin Kutrib.
144:No blind guessing should be required to solve a
423:International Conference on Fun with Algorithms
313:Mochikoro is a variant of the Nurikabe puzzle:
255:Further, consider these two rules of Nurikabe:
124:As of 2005, seven books consisting entirely of
320:All white areas must be diagonally connected.
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163:" logic to determine how they must grow.)
140:Solution to the example puzzle given above
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128:puzzles have been published by Nikoli.
30:Example of a moderately difficult 10x9
262:Black cells cannot form 2 Γ 2 squares,
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290:The binary determination puzzles
259:Black cells form a connected area
286:Solution to the previous puzzle.
278:An example 8x8 Mochikoro puzzle.
410:Brandon McPhail, James D. Fix.
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344:List of Nikoli puzzle types
51:Nurikabe, an invisible wall
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421:. Proceedings of the 3rd
244:Computational complexity
412:Nurikabe is NP-Complete
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98:Like most other pure-
67:Islands in the Stream
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449:Japanese board games
444:NP-complete problems
298:, also published by
47:determination puzzle
45:: γ¬γγγΉ) is a binary
21:Nurikabe (folklore)
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302:, are similar to
213:Advanced strategy
55:Japanese folklore
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16:Logic puzzle
334:Minesweeper
250:NP-complete
433:Categories
350:References
198:connected.
188:beginning.
49:named for
296:Mochikoro
392:16082806
328:See also
308:Nurikabe
304:Nurikabe
182:Nurikabe
153:Nurikabe
146:Nurikabe
126:Nurikabe
115:Nurikabe
106:puzzle.
104:Nurikabe
43:hiragana
39:Nurikabe
32:Nurikabe
425:, 2004.
110:History
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300:Nikoli
248:It is
231:black.
204:white.
119:Nikoli
59:Nikoli
34:puzzle
399:(PDF)
388:S2CID
380:(PDF)
161:atari
73:Rules
294:and
292:LITS
65:and
53:in
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157:Go
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41:(
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