Divided rooms

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Divided rooms
Divided rooms is played on a rectangular grid of cells with no standard size; the grid is divided into variously sized rectangular "rooms" by bold lines following the edges of the cells. Some rooms may contain a single number, typically printed in their upper-left cell; as originally designed, every room was numbered, but this is rarely necessary for solving and is no longer followed.

Some of the cells in the puzzle are to be painted black; the object of the puzzle is to determine for each cell if it must be painted or must be left blank (remaining white). In practice, it is often easier to mark known "blank" cells in some way—for example, by placing a dot in the center of the cell.

The following rules determine which cells are which:

Rule 1: Painted cells may never be orthogonally connected (they may not share a side, although they can touch diagonally).
Rule 2: All white cells must be interconnected (form a single polyomino).
Rule 3: A number indicates exactly how many painted cells there must be in that particular room.
Rule 4: A room which has no number may contain any number of painted cells, or none.
Rule 5: Where a straight (orthogonal) line of connected white cells is formed, it must not contain cells from more than two rooms—in other words, any such line of white cells which connects three or more rooms is forbidden.

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