# Heyawake

Heyawake is a type of shading logic puzzle published by Nikoli. The premise involve shading some squares that don't touch each other to fulfill the requirements for the unshaded cells and regions.

## Background

Heyawake was first introduced in Puzzle Communication Nikoli #39 in 1992, invented by Hiroyuki Fukushima. The name means "dividing rooms".[1] Traditionally, the rooms (marked regions) are rectangular in shape. When this constraint isn't followed, this is sometimes known as Heyawacky, a term first coined by Thomas Snyder in 2009. Such puzzles can also include internal borders as well.

### Other Variants

Ayeheya / Ekawayeh - Additionally, shaded cells in all rooms must be rotationally symmetric across the center of the room.

Akichiwake - First created by Prasanna Seshadri in 2014. Numbers instead denote the maximum size of contiguous unshaded cells in a given region.

Heyasleep - First coined by Prasanna Seshadri in 2012[2], although the variant is essentially equivalent to Heyawake. Later on, a variant with the same name by David Millar was created in 2018, with marked squares that signify being connected to only a single unshaded square.[3]. (Note that the pun only works orthographically, as heyawake is not pronounced like "awake".)

Heyacrazy - The heyawake "an orthogonal unshaded line cannot cross two borders" is generalized to include lines of any direction. First invented by Deusovi in 2019.[4]

## Puzzle Application

Heyawake is often presented in a grid subdivided into regions, some of which having numbers. These numbers indicate the number of shaded cells in that region. Additionally, shaded cells may not touch each other and unshaded cells must form a contiguous region such that a horizontal or vertical run of unshaded cells cannot cross over two region borders.

## Strategy

Many solve strategies involve marking cells that must be unshaded, which can be done at the start for cells containing a 0 or right after marking a cell that must be shaded. Marking unshaded cells allows for identifying runs of unshaded cells and unshaded cells that must have a way to "escape" in order to remain as one contiguous region.

Additionally, as shaded squares can never share a side with another shaded square, regions with numbers can have the shaded squares immediately deduced. For example, a 3x3 square marked with a 5 have the four corners and center marked as shaded, and a (2N-1)x1 rectangle marked with an N must have alternating shaded and unshaded with the shaded at the end. As more squares get marked unshaded within a region, the rest shaded squares can then be deduced by the no-adjacency rule.

TO DO