# Sudoku Techniques: Y-Wing

Learning to become a more proficient Sudoku player is highly rewarding, especially when you make use of well-known techniques that make solving the puzzle easier. Once you have a good grasp of the basic terms and mechanics of Sudoku, you can then try out these techniques and incorporate them into your solving style to solve medium Sudoku puzzles and higher difficulties.

There are many known tricks and techniques for Sudoku players that can make the puzzles easier to solve, and one of the most useful ones is the Sudoku Y-Wing. Using this technique can significantly increase your Sudoku puzzle-solving skill, and this trick is known to have created other derivatives.

What is the Y-Wing? Why is it called that and how does it work? Continue reading down below to learn more Sudoku tips and info!

## Terminology Refresher

There will be some terms here that may sound unfamiliar to you, here are some of them to help you understand:

### Box

A box is another name for a subgrid. There are nine boxes in the grid, and each box is a 3x3 square of nine cells. Some formats have them labeled 1 to 9, starting with the upper left corner and ending with the bottom right corner.

### Cell

Cells are the spaces inside the grid where numbers are written. There are nine cells in a box, and 81 cells overall in a grid.

### Column

Refers to the vertical cells that should hold numbers 1 to 9 without any repetitions. There are nine columns in a Sudoku puzzle. Some formats also have them labeled with numbers above and/or below the grid to make identification and navigation easier.

### Row

Refers to the horizontal cells that should hold numbers 1 to 9 without any repetitions. There are nine rows in a Sudoku puzzle. Some formats also have them labeled with numbers on the right and/or left side of the grid to make identification and navigation easier.

### Number/Letter Coordinates

If you’ve already jumped into a Sudoku discussion forum or read some Sudoku guides on a site, you might see some code-like words like r3c5, c5r2 or b1. Don’t get confused, as these are just numbering systems for a Sudoku puzzle. The “r” stands for “row”, “c” means “column” and the “b” means “box”. The number each means the label of the box, row or column to pinpoint the cell you’re looking for:

• Row 1 is the topmost row and row 9 is the bottommost row

• Column 1 is on the leftmost cell and column 9 is the rightmost cell.

• Box 1 is the upper left corner subgrid, and the count continues rightward, with box 3 as the upper right corner subgrid, box 5 as the center subgrid and box 9 as the lower right corner subgrid.

With this information, we can now know that the cell r3c5 is in row 3, column 5. We can also say that b1 is box 1, and is made up of cells between r1c1 to r3c3. This helps players immensely, especially when looking for a specific cell to fill or eliminate.

This is very similar to how Chess players call out their moves, like “knight to c6” or “pawn to g5”, or that time you were in school plotting angles using the X and Y axes.

## What Is the Sudoku Y-Wing?

### Origin of Y-Wing or XY-Wing

The Y-Wing, also called the XY-Wing or Y-Wing strategy, is an excellent candidate eliminator, regardless of a Sudoku puzzle's difficulty level. It's called as such because when the three cells used for the technique are connected with a line, it appears like an off-looking Y. However, it’s important to remember that every technique in Sudoku is limited in some sort of way. For Y-Wing, it only works on puzzles that have been sufficiently pencil marked with candidates. It also must meet certain conditions that we will explain shortly.

### Parts of the Y-Wing

To make it easy to understand, let's use this example puzzle:

Here we have cells marked, and they will form our Y-Wing pattern; r2c2 (3,8), r2c5 (3,6) and r8c2 (6,8). For the Y-Wing strategy or pattern, r2c2 is what we'd call the pivot, and r2c5 and r8c2 are the Y-Wings (also called "pincers").

### Two Cells and a Pivot Cell

Look closely and take note of the values and each position of all the cells. Some would call a cell with two pencil marks or notes in it a "bi-value cell", and if it would help you remember the technique better, feel free to write a candidate list with these.

If we were to draw figure lines between them, this is what the Y-Wing solution leads to:

### Theory Behind the Y-Wing

The Y-Wing is a candidate eliminator, so when properly used, it can solve a great deal more cells than you would by manually guessing. Think of it as knowing all the values in a triangle problem rather than just the corner.

Now, the theory behind it all revolves around one cell—the pivot cell, r2c2. If the pivot cell marked ab ove is of a certain value, then it'll eliminate the other candidates in the cells that it can "see"; which means that are in the same column, same row or same box/subgrid. Technically, it would also be correct to refer to these cells as a "locked pair"—r2c2 is locked with r8c2, r2c2 is locked with r2c5.

This elimination technique is effective as it clears out a lot of cells in one go, which is shown in this image:

### Affects Same Row, Same Column and Same Box

We know it might look confusing, but once we explain the theory further, it'll be easier to grasp.

Let's start with green. Green is r2c2, and whatever happens to it will affect box/subgrid 1, row 2 and column 2.

It's the same with blue, r8c2. Anything that happens to blue will affect box/subgrid 7, row 8 and column 2.

Then that's what happens to red, r2c5, as well. Any action made on that cell will affect box/subgrid 2, row 2 and column 5.

### Positional Examples

The Y-Wing strategy doesn't have a fixed range, as it could be like this with a cell in the bottom row of the lower left corner:

Or even like this as an inverted one:

All that matters is that the conditions for the Y-Wing to form are met, and the technique can be used.

### Conditions for the Y-Wing

Now, let's go back to our first puzzle example puzzle:

The first condition is that the three cells to be used in the Y-Wing must each contain two of three possible candidates. They will form the three corners needed to form the Y-Wing strategy.

The second condition is that the wings or pincers must see the pivot cell. The pivot cell is what relates all three cells, and it will also be the one to dictate what happens to the technique.

## How Does the Y-Wing Work?

Now to discuss how the technique works in the game!

The Y-Wing works by eliminating candidate numbers using logic around the pivot cell. Our pivot cell, r2c2, has candidates (3,8), while the two wings have candidates (3,6) and (6,8). If the pivot cell is assumed to have a value of 3, then we’ll eliminate candidate 3 in cell r2c5. If the pivot cell is an 8, then candidate 8 is removed in cell r8c2.

Again, to summarize, if r2c2 is 3, then r2c5 is 6. If r2c2 is 8, then r8c2 is 6. Regardless of whether one of the wings loses a 3 or an 8 in their candidate notations, the remaining candidate in that cell is guaranteed.

And since two cells now have an input, the remaining wing can be determined as well.

### Results of the Y-Wing Technique

Congratulations! You've done the Y-Wing! This ends in the elimination of more than two candidates and arriving at more than two guaranteed answers at the same time, helping you reach the final answer for your Sudoku game.

## The Y-Wing and Further Elimination

Another great aspect of this technique is that it eliminates other candidates in other cells within the same row, column and box/subgrid. In our example, since the numbers of all the Y-Wing cells have been determined, all of them clear out everything they can among the cells that they can see. This elimination also makes it easier for other techniques to take effect, as most of them also have their specific conditions to be performed.

Remember that in Sudoku, the more you eliminate candidates with accuracy, the faster you arrive at the correct answer. It doesn't matter if you can perform the technique properly. If the notations are wrong, you'll still arrive at an incorrect answer. So don't rush it and think carefully.