Heyawake Puzzles
Paint cells so every numbered room holds exactly that many, no two painted cells touch, the unpainted cells all stay joined — and no straight white run reaches across three rooms. Tap once to paint, again to mark a cell white. Every grid has one answer and needs no guessing.
Japanese for divided rooms, and sometimes printed as Hey Awake or Heya-wake.
Related Practice
What Is A Heyawake Puzzle?
Heyawake — Japanese for divided rooms — gives you a grid cut into rectangular rooms, some of them carrying a number. You paint cells until every numbered room holds exactly its number of painted cells. Painted cells may never share an edge, every cell you leave unpainted has to stay connected to every other, and no unbroken straight run of unpainted cells may reach across three rooms. It was devised by Nikoli, the Japanese publisher behind sudoku's popularity, and that last rule is what makes it its own puzzle rather than a variation on any other.
The Rule That Carries The Puzzle
Three of heyawake's four rules will feel familiar if you have played anything in this family. The fourth will not: a straight line of unpainted cells may not pass through three rooms. Follow any row or column, noting each new room the line enters; the moment it has entered a third, that stretch has to contain a painted cell.
This is the rule that makes a room with no number on it still worth something. Everywhere else in this family, information comes from counts. Here a good deal of it comes from where the walls are, which is why a heyawake with only a handful of numbers is still perfectly solvable — and why the grids on this page strip out every number they can.
Mark your white cells. You cannot see that a run reaches three rooms until you have committed to the cells in it being unpainted. The white marks are not bookkeeping — they are the thing the span rule reads. Solvers who only paint, and keep the rest in their head, stall on exactly this.
Where A Heyawake Opens
Every grid has a few rooms whose number and shape leave no choice at all, and they are the way in. Because painted cells cannot touch, a narrow room fills in only one way once its number is high enough for its size:
| Room | Number | Arrangements | What you learn |
|---|---|---|---|
| 1×2 | 1 | 2 | Nothing yet — but its neighbours often decide it |
| 1×3 | 2 | 1 | Both ends painted, middle white |
| 1×5 | 3 | 1 | Cells 1, 3 and 5 painted |
| 2×2 | 2 | 2 | One diagonal or the other — often settled from outside |
| Any | 0 | 1 | Every cell white, opening long runs for the three-room rule |
A room numbered 0 looks like it says nothing and is often the most useful clue on the grid. It hands you a block of white cells, and white cells are what the three-room rule feeds on.
Counting The Ways A Room Can Be Filled
When no room is completely forced, the next move is to take one small room and list every arrangement of its number that avoids two painted cells touching — including what its already-decided neighbours forbid. Any cell painted in every arrangement is painted. Any cell painted in none of them is white. This is the same reasoning a nonogram solver uses along a line, applied to a rectangle, and it is what the hint button here explains when it fires.
Which Rule Actually Does The Work
It is a fair question whether the three-room rule is genuinely central or just the unusual one. Because every grid here is solved by a program that records the reason for each cell it decides, the answer can be counted rather than guessed at. Across all sixty grids on this page — 2,550 individual deductions:
| Rule | Share of deductions | Grids it is needed on |
|---|---|---|
| Painted cells never touch | 36% | 60 of 60 |
| No white run across three rooms | 20% | 60 of 60 |
| A room numbered 0 | 18% | most |
| Counting a room's arrangements | 12% | 54 of 60 |
| Keeping the white cells joined | 9% | 57 of 60 |
| Plain room counting | 5% | most |
So the answer is yes: the span rule is needed on every single grid, and it is the second most productive rule after the basic no-touching one. A solver who never learns it is not going to finish a heyawake — which is also why it is worth marking your white cells as you go.
Why The Grids Stop At 7×7
Every grid on this page is proved before it is served: an exhaustive search confirms the answer is unique, and a second solver restricted to human reasoning has to finish it without guessing. Both proofs run in your browser at the moment the puzzle appears, so what matters is not the average time but the worst one. At 8×8 the average was fine and the worst case ran past a minute on unlucky room layouts. A page that occasionally hangs is worse than a page offering a slightly smaller grid, so the range here is 6×6 and 7×7, where every grid is built and proved in well under a second.
Heyawake Puzzles Frequently Asked Questions
What is a heyawake puzzle?
A logic puzzle on a grid divided into rectangular rooms. Paint cells so each numbered room holds exactly that many, no two painted cells touch, the unpainted cells all stay joined, and no straight white run crosses three rooms. The name is Japanese for divided rooms.
What are the rules of heyawake?
Four. A numbered room holds exactly that many painted cells; an unnumbered room may hold any number. Painted cells never share an edge. All unpainted cells form one connected group. And an unbroken straight line of unpainted cells may not pass through three or more rooms.
What does the three-room rule actually mean?
Follow any straight line of cells, across or down, noting each new room it enters. The moment it has entered a third room, that stretch must contain a painted cell. This is what makes an unnumbered room still say something.
Where do you start a heyawake puzzle?
With the rooms where the number and the shape leave no choice. A 1×3 room needing two has exactly one arrangement — both ends, because the two cannot touch. A room numbered 0 is equally useful: it opens long white runs for the three-room rule to bite on.
Why does marking cells white matter?
Because you cannot see that a run reaches three rooms until you have committed to those cells being unpainted. The marks are not bookkeeping — they are what the span rule reads. Only painting, never marking, is the commonest reason people stall.
Do the unpainted cells really all have to connect?
Yes — and it is a tool, not just an obligation. If painting a cell would cut some unpainted cells off from the rest, that cell must be white. Late in a grid, this one deduction often finishes the puzzle by itself.
Does every puzzle here have exactly one answer?
Yes, and it is checked twice: an exhaustive search confirms only one painting satisfies all four rules, and a separate solver restricted to human reasoning must finish without guessing. Grids failing either are discarded.
Why do the grids here stop at 7×7?
Because a page-load generator is judged on its worst case. An 8×8 builds, but some room layouts sent the uniqueness proof past a minute. At 6×6 and 7×7 every grid is built and proved in well under a second.
What does heyawake mean?
It is Japanese for "divided rooms", which is a fair description of the board: the grid is cut into rectangular rooms before anything is painted, and the rooms are what the numbers and the three-room rule both refer to. Without the room walls there would be no puzzle left at all.