How to solve Heyawake
Empty the 0 rooms, then let the walls do the work: a white line can’t cross two of them, shaded cells can’t touch, and the white cells must stay in one piece.
How it works
Heyawake gives you a grid split into rooms by thick walls. You shade some cells. A number in a room says how many of its cells are shaded. Rooms with no number can have any count.
Three more rules hold everywhere. Shaded cells never touch by an edge. All the white cells connect into one piece. And no straight line of white cells crosses two walls: that is the three-room rule.
Every puzzle here has a unique solution. You never need to guess, though harder days need a short try it and see.
An order that works
Start with the free moves: empty every 0 room, and shade any room whose number equals its number of cells that can be shaded.
Then walk the walls. Wherever a straight line runs from one room through the next into a third, at least one of those cells is shaded. When all but one are white, shade the last.
After each shaded cell, dot its neighbours. Before you shade a cell, check it doesn’t wall off some white cells. When nothing is left, suppose a cell is white and follow the rules until something breaks.
Worth memorizing
A 0 room is all white.
Dot every cell in it.
Next to shaded means white.
Shaded cells never touch by an edge.
A white line crosses at most one wall.
When all but one cell of a three-room line is white, shade the last.
Practice
0 of 4 rightAt the start, what is the ringed cell?
The 0 rooms are dotted. What is the ringed cell?
Using only the room numbers, what is the ringed cell?
What is the ringed cell?