Rectangle Rooms for beginners: one number, one matching area.
Learn how opposite corners define a room, practise a refused placement, and divide one checked four-by-four board into four rectangles with a complete area ledger.
Rectangle Rooms asks you to partition the whole grid into rectangles. Each room contains exactly one printed number. That number tells you its area in cells: width multiplied by height. Rooms cannot overlap, and no cell may be left outside a room.
Your decisions are areas of cells, rather than lines between dots or filled runs in rows. The common mechanic is described by Nikoli under the name Shikaku in source [1]. Our interface, clue placements and worked example are our own. No affiliation or invention of the common rules is claimed.
Read a number as area, not boundary length
A six can be two columns wide and three rows tall, or three columns wide and two rows tall, if that shape fits the board and contains no other number. A room does not have to be a square. One-row and one-column rectangles are allowed. A one-cell room is possible only for a clue of one.
Do not add several clues together to justify one large room. “Exactly one number” and “area equals that number” are separate conditions. Blank cells do not have a clue of zero; they can join the room of a nearby number. The finished partition must account for every blank cell too.
Make a room with two corner selections
Choose the first corner cell, then the cell diagonally opposite it. Both selected cells belong inside the rectangle, so count their rows and columns inclusively. R1C1 to R3C1 is one column and three rows, giving three cells. It is not two cells just because its endpoint row numbers differ by two.
The first selection receives an outline. It does not add a room or an edit. The second selection either places the rectangle or explains why it was refused, and clears the first selection. Either diagonal order works. Cancel first corner clears a pending selection without changing rooms. Selecting the same cell twice proposes a one-cell rectangle.
On a keyboard, use Tab to reach a cell and Enter or Space to select it. The arrow keys move focus to the neighbouring cell without drawing; they stop at the board boundary. Every label states row, column, clue and current room membership. Thick borders and the expandable Room ledger provide a check beyond room colours.
Load and inspect the beginner board
Choose Practice this example beside the article, or Load beginner board in the game. Check Edits 0 and no rooms. Read these four rows; a dot below means a blank cell, not a zero clue:
3 · 6 · · 3 · · · · · · 4 · · ·
The numbers total sixteen: 3 + 6 + 3 + 4 = 16. This is a useful consistency check because the four rooms must cover sixteen cells. It is not proof that any arrangement works, or that an arbitrary hand-made clue set has a solution.
Try a deliberately wrong proposal before solving. Select R1C1 and R1C2. The proposed rectangle has two cells but its sole clue is three, so it is refused at Edits 0. R1C1 to R1C3 is refused too: its area is three, but it contains two clues, three and six. A matching area alone does not make that second proposal valid. Retry this board before the complete route.
Place four justified rooms
Begin again at Edits 0. For each line below, select the two named cells once in the stated order. Check the inclusive dimensions before placing the room.
- R1C1 → R3C1. The top-left three can be a horizontal row of three or a vertical column of three. The horizontal choice would include the six at R1C3. Therefore its room is the first column from rows 1 to 3: 3 × 1 = 3 cells. Edits 1, three cells covered.
- R1C3 → R3C4. A six needs a 2-by-3 rectangle on this four-by-four board. A three-column, two-row rectangle containing the six would run across columns 1–3 or 2–4, including one of the threes. A two-column, three-row rectangle across columns 2–3 would include the central three. The remaining option is rows 1–3, columns 3–4: 3 × 2 = 6 cells. Edits 2, nine cells covered.
- R4C1 → R4C4. The bottom-left four could geometrically be 1 × 4, 2 × 2 or 4 × 1. The square or the vertical column would overlap the first room. Its room is therefore the whole bottom row: 1 × 4 = 4 cells. Edits 3, thirteen cells covered.
- R1C2 → R3C2. Only the upper three cells of column 2 remain. They contain the central three and form a 3 × 1 rectangle. This fourth room fills the last three cells. Edits 4, sixteen cells covered, four rooms and a complete partition.
Eight corner selections produced four edits because a room is committed only on the second selection. Refused proposals and a cancelled first corner add no edit. If you performed extra accepted placements or removals, Retry first rather than comparing their edit count with this clean route.
Reveal the complete room map and area ledger
Each letter denotes a room, not a number to enter:
A D B B A D B B A D B B C C C C
| Room | Corners | Rows × columns | Area |
|---|---|---|---|
| A | R1C1–R3C1 | 3 × 1 | 3 |
| B | R1C3–R3C4 | 3 × 2 | 6 |
| C | R4C1–R4C4 | 1 × 4 | 4 |
| D | R1C2–R3C2 | 3 × 1 | 3 |
The room areas total sixteen. Each contains one of the four clues, the rooms do not overlap, and every cell belongs to exactly one room. This clue set was independently checked for exactly one complete valid partition.
Practise Undo, removal and retry separately
After the win, the cell buttons lock and focus moves to Undo last edit. Undo once removes room D, returning to Edits 3, three rooms and thirteen covered cells. The missing cells are R1C2, R2C2 and R3C2. Place that same room again to finish, or Retry this board to start at zero with unchanged clues.
For a removal experiment, Retry and place only room A. Select Remove a room, then any of its cells, such as R2C1. The whole rectangle disappears and Edits becomes 2. Undo once restores room A at Edits 1. Removal mode remains active after that Undo; select Remove a room again to return to drawing, or use Retry, which also returns to drawing. Selecting an unassigned cell in removal mode changes no room and adds no edit.
Reveal the control and rule self-checks
Does selecting R3C1 before R1C1 change the proposed room? No: the same two corners describe the same three cells. Can two numbers share a room if their sum equals its area? No: the room must contain exactly one printed number. Does a first-corner selection prove the proposed rectangle is legal? No: the rectangle is checked after the second corner. Does a locally accepted room prove the rest of the board can be finished? No: local checks do not search for a compatible complete partition.
Know what a new attempt changes
Load beginner board restores this exact example. Retry keeps the current clues and clears all rooms, history, selection and removal mode. New puzzle changes to another prepared clue set in the finite seven-puzzle collection; the collection repeats. A fixed practice address reloads this example after refresh, but it does not save your rooms or edit history.
There is no timer, account, payment, saved leaderboard or advertisement action required. Your room choices stay in this browser tab and are not submitted to the server. This tutorial teaches how to read and check a partition; it does not promise a health benefit, a measured difficulty level or a general improvement in ability.