How To Solve Nurikabe Puzzles
Nurikabe is a classic Japanese “island-building” puzzle from the same family of logic puzzles as Sudoku and Kakuro.
Puzzle
The puzzle is typically played on a rectangular grid of cells. Some cells contain a number indicating the size of the island they are a part of.
The basics of the game are to shade cells to divide a grid into specified-sized regions of sea and islands.
Solution
Cells are initially of unknown color but can only be shaded or white. Two same-color cells are considered "connected" if adjacent vertically or horizontally but not diagonally. Connected white cells form "islands," while connected shaded cells form the "sea."
The challenge is to decide if each cell is white or shaded according to a set of rules.
Look for numbers that are close to each other. Since each number must have its own island and each island cannot touch each other (except at a corner), the cells between must be shaded.
Rules
A numbered cell indicates the number of cells in that island and is itself one of the island cells.
Each island can contain only one numbered cell.
Two islands may not be connected either vertically or horizontally. They may touch at the corners.
There can only be one sea in the puzzle, so all shaded cells must be connected.
There cannot be any 2x2 areas of shaded cells.
Common Techniques
Some solvers “dot” the non-numbered cells they have determined to belong to an island
Until the solver is sure that a cell is part of the sea, light shading that can be easily erased is recommended.
Basic Strategy
Look for cells marked with “1”. Since these islands are only one cell in size, all the adjacent vertical and horizontal cells must be shaded (not diagonal).
The space marked "2" must have a corresponding island space above or to the left of it. Since islands cannot touch, the space diagonal to the "2" must be shaded.
Since all shaded cells must be connected in a single group, no shaded cell can be isolated. Look for these cells and expand them horizontally or vertically.
Look for unreachable cells. In this case, the red squares are beyond the maximum reach of any number and are shaded in.
Other unreachable cells.
Look for areas where the correct number of island cells are identified and shade the unneeded cells.
Look for numbers that are close to each other. Since each number must have its own island and each island cannot touch each other (except at a corner), the cells between must be shaded.
WIth the rule prohibiting 2X2 shaded cells, the cells with the red dot must be islands and not shaded.
Look for lone island cells and fill them in.
This completes the "4" island so the two cells below can be shaded.
Once an island is "complete" (it has all the white cells its number requires), all cells that share a horizontal and vertical side must be shaded.
Finally, the two red cells are unreachable and are shaded. The cell marked with X is shaded due to the "no 2X2 rule". That leaves the cell below the "2" as the last island cell.