Nurikabe Rules

A Nurikabe is a Japanese spirit that manifests itself as a wall to impede travelers walking at night. The puzzle Nurikabe is so named because the object is to figure out where the black cells are placed based on the clues.  I guess the black cells are the Nurikabe spirits.  Here are the rules and a sample puzzle:

1. Each number in the grid indicates a region of edge-connected cells of exactly that number.  No two numbered areas can touch except at corners.  Each number will be a part of exactly one region

2. Each numbered region is surrounded by either the walls of the puzzle, or black cells.  All black cells must be edge-connected together to form one contiguous region.

3. No numbered cells can be painted black.

4. No black cells can be connected together to form a 2x2 area of black cells in any part of the grid.