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# Nurikabe rules

The rules to Nurikabe are actually quite simple, but they combine together to give some wonderful logic problems. The challenge is to construct a maze (where the white squares are the walls), that satisfy these rules,

- The walls are made of connected adjacent stone blocks.
- The squares with numbers in them are part of a wall. That particular wall must contain exactly that number of squares, e.g. A square with the number 4 in it means that it forms a wall with 3 other squares.
- Walls may not touch each other, even if they have the same number (diagonally is fine).
- All the squares that are not part of the wall make up the maze.
- The maze must be one single connected whole, i.e. from any black starting square, you must be able to reach any other black square by only moving to adjacent black squares. Diagonal moves are not allowed.
- The maze can't contain any 2*2 'rooms'

A completed Nurikabe puzzle,

From this set of rules, we can make a few deductions,

- Once a wall has it's correct number of squares, all the squares around that wall must be black.
- As a special case of the first rule, if we see the number '1' in a square, then all the squares next to that square must be black. This is usually how we start a Nurikabe puzzle.
- If we see two squares with numbers diagonally from each other as in this example:

then for those two walls to be seperated, the other two squares in this example must be white. - If we see three black squares forming an 'elbow' like this,

then we know the other square in this image must be white to avoid breaking rule 6. - All black squares must be connected, so if there is an undecided square(s), and if the only way to connect two seperate areas of black squares is for the undecided square to black, then that square must be black.
- All white squares eventually belong to a wall. So if we have an isolated white square, and there is only way for it to connect to a wall, then those squares must be white.
- You will sometimes find some undecided squares that cannot be reached from any island, or in doing so would break another rule, then in that case, that square must be black.

These rules take a little bit of getting used to, but once you are familiar with them, Nurikabe puzzles offer a good alternative to the more mainstream logic puzzles such as Sudoku. Want to see how these rules are applied to solve a Nurikabe puzzle?