Evil Heyawake

How to solve a heyawake

The grid is cut into rooms. Shade squares so that a numbered room holds exactly that many shaded squares, no two shaded squares touch side by side, the unshaded squares all join up, and no straight run of unshaded squares crosses two room walls.

The method

1. 1Start with the rooms numbered zero. A 0 means nothing in that room is shaded, which is free information and usually opens a corner. A room whose number equals the most it could possibly hold is just as free: in a room one square wide, a number that fills every other square leaves no choice at all.
2. 2Count the rooms a run crosses, not the squares. This is the rule the whole puzzle turns on and the one beginners skip. Look along any row or column: if three squares in a row would be unshaded and they sit in three different rooms, one of them has to be shaded. It works in rooms with no number at all, which is why most of the board can be blank.
3. 3Shade one square and you have ruled out four. Shaded squares never touch side by side, so every square you shade makes its four neighbours unshaded. Mark them, because those unshaded squares are what the run rule reads next.
4. 4Keep the unshaded squares joined up. They have to form one single region at the end. If shading a square would wall a group of unshaded squares off from the rest, it cannot be shaded, however well it suits the numbers.

The one rule people get wrong

The run rule counts ROOM WALLS crossed, not squares. A run of six unshaded squares is perfectly legal if they all sit in one room, and a run of three is illegal if it touches three rooms. That is why the walls are printed heavier than the grid.

What the answer page shows

The same grid with every shaded square filled in. Where a number sits on a square the answer shades, it is printed in white so you can still read it.

How the grades differ

A bigger board cut into more rooms, with more of those rooms left without a number. The easy grades number most rooms; the hardest leaves two thirds of them blank and leans on the run rule instead.

Is it the same as nurikabe?

No. Both shade a grid and both keep the unshaded squares connected, but in nurikabe the numbers give the size of unshaded islands and the shaded squares are meant to join up, while here the numbers count shaded squares inside a room and it is the shaded squares that may never touch.

Good for

Anyone who likes a rule that rewards looking along a line.