Mochikoro

Mochikoro ("Mochinuri") is a logic puzzle. It consists of a grid, with numbers in some cells. The aim is to blacken some cells according to the following rules:

• The black cells divide the grid in rectangular areas ("islands") of white cells.
• No two islands may share an edge, but all of the islands must be connected to each other through their corners.
• Each numbered cell must be a part of a white island. Some white areas may not include a cell with a number.
• Each island must have the same number of white cells as the number it contains (including the numbered cell).
• 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.