From the rulebook
How to Solve Heyawake
Heyawake is a logic puzzle played on a grid divided into bold-outlined rectangular rooms. You shade cells black so that every numbered room holds exactly that many black cells, no two black cells share an edge, all white cells stay connected, and no straight white line runs through three or more rooms. This guide takes you from the rules to the techniques that crack hard grids without guessing.
The rules of Heyawake
A Heyawake grid is split into rectangular rooms with bold walls. Some rooms show a number, the exact count of black cells that room must contain. Rooms without a number may hold any number of black cells, including none.
Three placement rules govern every board. Black cells never share an edge, though touching at a corner is fine. Every white cell must connect to every other white cell through edge-to-edge white neighbors, so the white area is one piece. A straight horizontal or vertical line of white cells may pass through at most two rooms, so any run that would cross into a third room must be broken by a black cell.
Read numbered and unnumbered rooms
A room's number counts every black cell inside its walls, wherever they sit. Because blacks cannot touch edge to edge, a number close to half the room's area forces a checkerboard-like spread, which pins many cells immediately. A 2 in a 1 by 3 room, for example, must occupy the two end cells, leaving the middle white.
Unnumbered rooms are not empty rooms. They take whatever black cells the connectivity and line rules demand. Treat them as flexible space, and come back to them once the numbered rooms and line breakers have shaped the board around them.
Open with zeros and one-cell rooms
A room numbered 0 is all white, so mark every cell in it white right away. Those whites feed the line rule, because a fully white room makes any straight run through it more likely to span three rooms and need a breaker nearby.
A 1 by 1 room numbered 1 is a guaranteed black cell, and every cell around it that shares an edge becomes white at once. These direct reads cost nothing and often unlock the first line-rule deductions of the solve.
Let black cells force white neighbors
Every time you confirm a black cell, mark its edge neighbors white. This is the most frequent deduction in the puzzle, and skipping it hides easy progress. A confirmed black in a tight room can settle the rest of the room's count on the spot.
The forcing works in reverse too. If shading a cell black would trap a white cell with no white neighbor left, that cell must stay white. Watch corners and cells beside existing blacks, where one more black can strand a lone white.
Break long white lines
The line rule is Heyawake's signature deduction. Take any straight row or column segment of white cells and count the rooms it passes through. The moment a run would cross into a third room, one of its cells must be black. When only one cell in that stretch can legally take a black, that cell is forced.
Scan every row and every column for these stretches after each placement. A black placed for a room count often shortens one line while lengthening the pressure on another, so the line rule keeps paying off all game.
Enumerate patterns inside a numbered room
When a room's number does not pin its cells outright, list the legal ways its blacks can sit. Blacks cannot touch edge to edge, so a 2 in a 2 by 2 room must use one of the two diagonals. If every legal pattern agrees on a cell, that cell is decided even though the full pattern is not.
Combine the patterns with the room's surroundings. A pattern that would edge-touch a confirmed black outside the room is illegal, and a pattern that would cut off a white pocket is illegal too. Crossing off patterns this way often collapses a room to a single arrangement.
Guard white connectivity
Every white cell needs a route to the rest of the whites. A white pocket with one remaining escape cell keeps that escape white, since blacking it would seal the pocket off. Watch the cells along walls and beside black pairs, where escapes run out fastest.
Some cells are articulation points, single cells whose loss would split the white area in two. An articulation cell can never be black, no matter what the room numbers suggest. On hard boards, spotting these cut points is what separates a stall from a breakthrough.
Combine rooms, lines, and connectivity
The hardest deductions come from stacking the rules. A room pattern that satisfies its number might still be impossible because it seals a white pocket, and a line breaker might have only one legal home once room patterns are crossed off. Cycle through the three rule families in turn, room counts, line breakers, then connectivity, and each pass tightens the next.
On Puzzle Lair every Heyawake puzzle is guaranteed solvable by logic alone, so if you are stuck there is always a deduction waiting, never a guess. Heyawake is currently marked beta, so rules and tuning may still change as the puzzle is tested.
Work through a small example
Picture a 6 by 6 board whose top-left room is 1 by 1 and numbered 1, sitting beside a 1 by 3 room numbered 2 and above a wide unnumbered room. The 1 by 1 room is black immediately, so its right and lower neighbors are white. The 1 by 3 room's 2 must use its two end cells, because two blacks cannot sit side by side, so its middle cell is white.
Now the line rule takes over. The whites forced along the top row form a straight run that already touches two rooms, so the first cell past the next wall must be black or the run would span three rooms. That new black forces its own neighbors white, the neighbors feed the next line check, and the chain of room counts, breakers, and connectivity carries the board to its single solution.
Frequently asked questions
- Can an unnumbered room contain black cells?
- Yes. A room without a number accepts any count of black cells that the other rules allow, including zero. Only numbered rooms fix an exact count, so treat unnumbered rooms as flexible space shaped by the adjacency, connectivity, and line rules around them.
- Can a numbered clue cell itself be black?
- Yes. The number is printed in one of the room's cells, but that cell follows the same rules as any other cell in the room. If the room's legal pattern puts a black on the clue cell, shade it. The number still counts every black in the room, including its own cell.
- Do I have to mark white cells?
- No. White marks are a note-taking aid, not a requirement. The puzzle is complete when the black cells match the solution, so unknown gray cells and marked white cells are interchangeable at Check. Most solvers still mark whites, because confirmed whites drive the line and connectivity deductions.
- Can black cells touch diagonally?
- Yes. The adjacency rule only forbids black cells that share an edge. Two blacks meeting at a corner are legal, and diagonal chains of blacks are a common sight in solved boards.
- Does every Heyawake puzzle have exactly one solution?
- Yes. Every Puzzle Lair Heyawake puzzle is generated and verified to have exactly one solution reachable by pure logic. Being stuck means there is a deduction you have not spotted yet, often a line breaker you have not counted or a white pocket about to lose its last escape.
- What does Check do in Heyawake?
- Check tests your current black cells against the solution and reports whether the board is solved. There is no live feedback while you play and no mistake limit, so you can experiment freely and press Check whenever you think the shading is complete. A failed Check simply says the board is not solved yet.