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A Nikoli logic puzzle whose name means “divided rooms”. Shade cells so every numbered room holds exactly that many, with no two shaded cells touching, every white cell joined in one network, and no straight line of white cells running through three rooms. Each 7×7 board has exactly one solution, and your time is your score.
The 7×7 grid is divided by bold lines into rectangular rooms. Some rooms show a number in their top-left corner: that room must contain exactly that many shaded cells. Rooms without a number may hold any amount, including none.
Three more rules apply everywhere. Shaded cells may never share a side with each other, although they may touch at a corner. All the white cells must form one connected area, so a shaded cell can never cut part of the grid off. And a straight horizontal or vertical line of white cells may cross at most one bold border — it can pass from one room into the next, but not on into a third.
Tap a cell to shade it. Tap it again to put a dot in it, which marks a cell you know is white, and a third tap clears it. Numbers turn green when their room is exactly right and red when it holds too many. Shaded cells that touch turn red, a line of dotted white cells that passes through three rooms turns red, and white cells that have been walled off from the rest show a red dot.
The clock starts when the board appears and stops the moment every rule is satisfied. Each board has exactly one solution, and your time is your score.
Start with the zeros. A room marked 0 is entirely white, so dot every cell in it straight away — those dots often force shading in the rooms next door, because a long white line leaving a zero room can only cross one more border before something has to stop it.
The three-room rule is the engine of every solve. Whenever a row or column of white cells is about to stretch from one room, through a second and into a third, some cell along that stretch must be shaded. If only one cell on the stretch is still undecided, that cell is black. Look especially at narrow rooms one cell wide, where a line crossing them touches three rooms very quickly.
Every shaded cell immediately makes its four neighbours white, and the connection rule does the rest: never shade a cell that would seal off a white corner or split the board in two. Cells along the edge are the usual culprits — a shade in the corner's diagonal pair can trap the corner cell.
Small numbered rooms are easier than they look. A 2 in a room of three cells in a row has only one answer, the two ends, because the middle cell would touch either of them. A 1 in a 2×2 room is weaker, but combined with a neighbour's forced shade it usually settles quickly.