Nurikabe is one of my favorite puzzle. This is becoming as popular as Sudoku, Kakuro or Slither Links puzzle.
Nurikabe (hiragana) is a binary determination puzzle named for an invisible wall in Japanese folklore that blocks roads and delays foot travel. 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.

Rules of Nurikabe
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 cells form "walls", while connected black cells form "a stream".
The challenge is to paint each cell black or white, subject to the following rules:
Each numbered cell is a wall cell, the number in it is the number of cells in that wall.
Each wall must contain exactly one numbered cell.
There must be only one stream, which is not allowed to contain "pools", i.e. 2x2 areas of black cells.
Human solvers will typically dot the non-numbered cells they've determined to be certain to belong to a wall, while trying to solve the puzzle.
Like most other pure-logic puzzles, a unique solution is expected, and a grid containing random numbers is highly unlikely to provide a uniquely solvable Nurikabe puzzle.

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