1. Determine whether each cell is white or black according to the following rules.
2. The black cells must all be connected to each other through their edges. No 2x2 cell area within the grid can contain all black cells.
3. Cells with numbers in them cannot be black.
4. Every cell with a number in it must be part of a polyomino-shaped "island" containing that number of white cells. No two islands may be adjacent horizontally or vertically. Every island must contain exactly one number. Every white cell must be part of exactly one island.