Cocktail Lamp

Cocktail Lamp ("Kakuteruranpu") is a logic puzzle. A rectangular or square grid is divided into regions. The goal is to blacken some cells of a grid according to the following rules:

• All black cells in a region must be connected horizontally or vertically (they form a "block").
• A cell with a number indicates how many cells in the region must be blackened.
• In a region without a number any amount of cells may be blackened (all cells may stay white).
• When two cells are orthogonally adjacent across a region boundary, at least one cell must be white.
• All blocks of black cells must be connected to each other through their corners.
• No 2 x 2 cell area within the grid can contain all black cells.

Cross+A can solve puzzles from 3 x 3 to 30 x 30.