Look-Air Exploration

In this post, we'll take a deep dive into the rules of Look-Air, a puzzle genre by Nikoli. Examples and visuals will be included.

Part I: Setting the Scene

To start, here are the rules, according to this dictionary:

"Shade some cells so that each orthogonally connected area of shaded cells is in the shape of a square. Clues represent how many of the five cells forming a cross around the clue (including itself) are shaded. Two shaded squares of the same size may not have a vertical or horizontal line of unshaded cells between them, unobstructed."

Let's break down each of these rules step by step:

1. "Shade some cells so that each orthogonally connected area of shaded cells is in the shape of a square."

    On the grid, each cell can take one of two states --- shaded or unshaded. If you know that a cell is unshaded, interfaces tend to use green, and if you know that a cell is shaded, interfaces tend to use black or dark gray. White is also used to show cells where the state is unknown.

     Each mass of shaded cells must form a filled square as well (so a 1x1, 2x2, etc.)

    In the image, the right figure has a known unshaded cell in the middle of the "square", so it isn't allowed.

2. "Clues represent how many of the five cells forming a cross around the clue (including itself) are shaded."

    

    In Look-Air, clues are numbers, and they count how many of the cells orthogonally adjacent to it and itself are shaded. Unlike other shading genres, clues are allowed to be shaded. You can refer to the image for a visual guide. 

3. "Two shaded squares of the same size may not have a vertical or horizontal line of unshaded cells between them, unobstructed."

    Basically, two squares of the same size cannot "see" each other, unless obstructed by another square of a different size.

    For example, in the above image. the left figure shows two 1x1 squares that have a direct view of each other. In the right figure, the 1x1 squares are still shown, but a 2x2 square is blocking their view.

Part II: Basic Logic (without clues)

Here’s some basic facts and figures.

Any mass of shaded cells that isn’t already a filled square must form a filled square.

If any side adjacent to a square has some unshaded cells on it, then those unshaded cells can extend to fit the entire side.

Any square limited on two opposite sides is limited on all four sides.

Part III: Number Logic (with only 1 clue)

Let's take a deeper dive into clues now.

The above image shows the guaranteed states (shaded/unshaded) of some numbers. Here are some explanations on why some numbers must be shaded and some must not. Note that the visuals show examples of possible shadings near the number.

0: Must be unshaded. The cross surrounding the 0 must be unshaded as well. Focusing on the clue itself, if the 0 is shaded, it would contradict itself.

1: Could be either shaded or unshaded. However, if the 1 is shaded, it must form a 1x1 square. Generally, 1s will be unshaded.

2: Must be unshaded. If the 2 was shaded, another cell orthogonally connected to the 2 also must be shaded. This will cause the other squares to get unshaded, effectively breaking the rule of squares.

3: Could be either shaded or unshaded. If the 3 is unshaded, it must border either 1 or 2 1x1 squares. If the 3 is shaded, it must form at least a 2x2 square.

4: Must be shaded. It also must be on the edge of a 3x3 or larger square. If the 4 was unshaded, two pairs of 1x1 squares would see each other.

5: Must be shaded. The cross surrounding the 5 must be shaded and also must expand to form at least a 3x3 square. If the 5 was unshaded, it would contradict itself.

Part IV: Number Logic (with multiple clues)

Next, here are some patterns that you might see and rules for those patterns.

Any number that already has the correct number of shaded/unshaded cells can have the rest of their cells shaded/unshaded based on the number.

A 3 backed into a corner must be shaded, and it must form at least a 2x2 square.

A 3 backed into an edge follows the same rules, however, it can expand in either direction.

A 2 backed into a corner must border two 1x1 squares.

If a 1 orthogonally borders a 4, then the 1 and all the cells orthogonally bordering the 1 (except the 4) must be unshaded, and the 4 forms an edge of a 3x3 square or larger.

If the areas of at least two 5s touch based on the 3x3 area centered around the 5s, then they all form a large square (which varies based on how much the 5s are spread out and how many 5s are present)

This next pattern is similar to a "1-2" in minesweeper and happens when a 2 touches an edge and a 1 is diagonally adjacent to the 2. The cells that the 1 can see but the 2 can't are unshaded, and the non-2 cell that the 2 can see but the 1 can't is shaded. The other cell that is shaded depends on if the top cell expands or not.

If it expands, the top pattern on the next image applies. Otherwise, the bottom pattern on the next image applies.

Example Puzzle 1

Now that I've explained some basic Look-Air logic and patterns, it's time for some example puzzles! My time on this first puzzle is 6 seconds, but if you've followed along well, you can pretty easily solve this puzzle in under 30 seconds. Note that you don't have to beat the creator's time or target time, as these are just examples.

I don't recommend using this post as a cheat sheet for the example puzzles, but you can study it before solving. Solutions to all example puzzles will be at the bottom of this post.

To use the interface, left click to shade a cell, and right click to unshade a cell. On mobile, tap once to shade a cell, and tap twice to unshade a cell.

Difficulty: 0/14

Online interface (puzz.link)

Example Puzzle 2

This one's also a 5x5, but slightly harder.

Creator's time: 0:08

Target time: 0:45

Difficulty: 1/14

Online interface (puzz.link)