Unlocking the Secrets of Sudoku: How to Locate the Elusive Y Wing

Are you a Sudoku enthusiast looking to up your game?

We explore the fascinating world of Y Wing in Sudoku. From understanding what a Y Wing is to learning how it works, identifying it in a puzzle, and using it to solve Sudoku, we’ve got you covered.

We’ll share some tips and tricks to help you master this advanced solving technique. So, grab your pencil and get ready to elevate your Sudoku skills!

What is Sudoku?

Sudoku is a logic-based, combinatorial-configuration, placement puzzle that was invented in 1783 by Swiss mathematician Leonhard Euler. The modern puzzle was created by Howard Garns in 1979 published by Dell Magazines as Number Place. It was later extended, simplified, and popularized by Wayne Gould. Indeed, Sudoku has been around for a long time. Despite this, not much is known of its history between Euler and the publication of the Dell puzzle in the US in 1979.

What is a Y Wing in Sudoku?

A Y Wing in Sudoku is a type of XYZ-Wing pattern of elements. In this case, the elements are individual cells in a Sudoku puzzle, and the key implication of the Y Wing is the simple T-Shape that gives it its name. The Y Wing is a chaining technique used to uncover candidate elimination opportunities in cells that cannot be solved using normal techniques. These unique patterns of chains and grouped weak links form a medium-to-difficult level of solving Sudoku puzzles and often result in highly challenging and complex puzzles being solvable.

The set-up of Y-Wing patterns of cells is that three bi-value cells are needed. That is, each Sudoku cell making up the formation can only have two possible values. Straight lines of weak links formed by bi-value cells give the Y-Wing pattern a series of forcing chains stretching from square to square. Once the Y-Wing cells are set up, the three cells in the pattern must have a relationship and be chained in such a way that they set up if-then opportunities for other cells in the puzzle when one or more elements are solved or eliminated.

How does a Y Wing Work?

A Y-Wing in Sudoku is a complex chain mechanism where three squares have exactly two possible values. If one of the two valued squares is positive to the solution, it forces the other two squares to be negative to the solution. This must occur no matter which solution value is positive. In this case one of the two undetermined squares will be forced to be positive to the solution in order to resolve the contradictions arising from all three squares being positive. The best way to understand Y-Wing is through an actual completed Sudoku puzzle.

7, 0 and 9 are the possible solution values for squares A3/C3, A2/B2 and C2. If A2 is 0, then 7 and 9 must be in C3 and C2, meaning that neither 7 nor 9 can be in B2.

What are the Benefits of Knowing Y Wing in Sudoku?

The benefits of knowing Y-Wing in sudoku are that it may be useful on harder puzzles, certain chaining puzzles with a long AIC, and some puzzles with symmetry. Y Wings can make a puzzle much easier and quicker to solve by highlighting a contradiction or quickly allowing for elimination possibilities.

How to Identify a Y Wing in Sudoku?

You identify a Y Wing in Sudoku when you have three unanswered cells numbered from 1-9. In a Y Wing, at least two of the three cells are connected to the same block by two lines. In the third cell, the line is joined to the other two blocks. If all three cells are connected to the same three different blocks, it is not a Y Wing.

There are two base Y Wing patterns to look out for. The first is to look for two cells to be connected in a single block and the third to be connected in each of the other two different blocks. Both leading back to the same candidate (ZD Guides). The second is to look for three cells forming a Y. When one of the exclusive cells turns out to be a candidate. For example, cell x and Y are connected to the same cell that is either x or y (ZD Guides).

Step 1: Look for a Y Wing Pattern

Look for a Y Wing pattern in a puzzle. A Y Wing pattern consists of three cells that make up a triangle. Two corners of the triangle will be the initial candidates. We can trace a short Y-shaped chain connecting the two corners. The third cell represents the base of the Y. One tip for recognizing Y Wings patterns is to trace two candidate numbers in all possible ways on a 3×3 square to understand that if we build a chain connecting the candidates, the third cell is occupied by the base.

Step 2: Identify the Base Cell

The base cell B is an arbitrary placement of a cell within the block that contains both digits of the double occurrence. A base cell equivalent to Graph A’s X in the location of R1C1 would have at least one of the two digits of the double in itself. It may have the other digit, but not necessarily. The base cell is foundational to the entire logic of the Y-wing. It is the first step of the pattern that appears again and again in the different solving steps.

Use the double clue digit to identify the cell in the original block which contains both the real and possible instances of the double clue. This is the equivalent of Y-wing pointing in Anne’s Magic. In a language com-run from the point. Whether from the base cell or not from the base cell.

Step 3: Identify the Wing Cells

The wing cells are the cells connected by the same set of two candidates in two different unit intersections. Ignore any cells with more than 2 candidates in them including the tip cell where Y originates as one of its candidates. The wing cells are the two cells that have candidates A and B located in 2 different unit intersection lines based on a pattern created by the tip cell:

• If the tip cell is in the middle cell of one side of a unit intersection, the other cells are the other 2 corner cells.
• If the tip cell is in one of the corner cells of a unit intersection, the other cells are the opposite corner cells.

You want the two cells to be linked by something other than your two initial candidates in them. The wing cells should begin as yet unfilled cells. Only after you confirm the wing cells under this pattern can you selectively look for the extra candidates that are needed to create a locked candidate effect, either in the unit intersection they share. Or, more importantly, between the wing cells.

Note: Tursupa95’s original Y Wing video on his YouTube channel points out an example that differentiates the wing cells connected by set of extra candidates versus the wing cells that would not form two extra candidates of the same number in the unit intersection. Watch the video embedded above to observe the notation and pattern which can be extremely useful when learning how to find a Y Wing. He actually uses a wrapped pattern of arrows to identify the spotted cells.

Step 4: Check for Elimination Possibilities

With regions 3 and 8 making regions 1 and 2 an empty subset of the grid, all of their candidates except {7} get eliminated. The same is true for regions 6 and 9. By focusing on the nested regions 1-3 and 7-9, we have eliminated all but {7, 8} for the cells in these regions. This now verifies the Y-Wing constraint.

How to Use Y Wing in Solving Sudoku?

You use Y wing in solving Sudoku by gradually analyzing rows, columns, and common squares until you find the pairs of cells needed for Y wing diagrams to uncover a hidden triple, hidden pair, or confined number trick. Here are some step-by-step pointers to use Y wing effectively during Sudoku gameplay.

Basic Y wing steps:

• Always prioritize Y wings with fewer degrees as they are easier to spot.
• If the Y wing cells all have strong links, the point cells can be a cell with a weak link that is linked to all Y cell cells and shares the same number with the Y wing.
• Remember that, at the final point of the Y wing, the deduction is made with an AIC whose endpoints are on the same number.
• When searching for spot cells, check for the same number on all three Y wing cells, as it will break the Y wing, usually revealing the hidden pair or showing constraints such that other pieces are known socer simultaneously.
• If you cannot find spot cells, look for three link cells that contain valid candidates that are solved before the Y wing is found. The only other alternative is to look at the three-digit numbers and find a slash with the second Y wing so that a pair or hidden pair is discovered.
• Check the spot cell to make sure that when it is solved, the Y wing can solve a puzzle.

Step 1: Identify the Y Wing Pattern

The Y Wing cell is a hidden matching set of candidate squares in three squares that form the hook of a Y. It gets the hook shape because two of the squares are in complementary squares. All three squares must see the same square, the Target Square, as their peer. The Target Square should only have a candidate as in screenshot 1 for step 1 below. This method of finding a Y Wing special scenario is necessary for it to work.

If we name all cells which can see two pairs of cells in the Y and other cells can’t see any of the pairs, we get the diagram in screenshot 2 below. For a Y Wing to be useful, one of three squares needs to have exactly two candidates. That candidate must appear in each empty fellow square in either of the other squares.

There are many cells where two unique candidates create a Y Wing, such as in this chart. The target square can never have more than two squares or it won’t work. Diagrams 2-4 show typical patterns of the Y Wing, including a V shape, a twisted 3-chain, and a more widely spread V formation.

Step 2: Look for Elimination Possibilities

With the Y-Wing pattern identified and the three cells in the angle’s three corners featuring the coloring digits, check what other cells that are eliminations of certain numbers. If another cell is in the same column as one corner cell, another one in the row of the other corner cell, then any other number placed in the row would either remove the pattern sighting, remove the elimination, or both.

If this logic holds true, then the other cell features a third number that is a part of the pattern. You can try to test the solution by inputting the third number and then working backward, seeing if you can find a contradiction. If so, keep identifying all the cells that the Y-Wing would have an effect on, and the 3rd number will show itself.”””

For this sudoku, since we made the assumption at the start that cell 2 in column 1 was a yellow 4 or 5, let’s assume that is a yellow 5. Using that and all of the logic we have stated above, we can find the answer to the following sudoku from solvers and it matches the yellow pattern:

Step 3: Apply the Elimination Possibilities

Apply elimination possibility methods until you find the Y Wing in order to solve the difficult sudoku puzzle. Many free sudoku puzzles that appear easy at first require methods such as block intersection, Naked Pairs, Swordfish or Jellyfish in order to reach the solution.

After marking the candidates in pencil as mentioned in the previous examples, check if the outer candidates of the fish are part of line boxes 5 or 2 (blocks 1, 3, 5). Since neither 3 nor 2 contain positions for both 1 and 5, it is impossible for both the Intersection and Box/Line Reduction Rule to be satisfied at the same time. At least 1 of the 2 deductions must be true, which implies the opposite is false by the Law of Complementarity.

Go back to the pencil marks of the fish in question and reevaluate other techniques of fish, especially if other outside fish pairs have significant numbers with intersecting blocks. Or as is the case in the photo below and tends to be common in the Diabolical level puzzles, the fish in question could have nothing to do with the solution, and one of the other techniques that has emerged from the created pairs could deliver the solution to the puzzle.

Tips and Tricks for Finding Y Wing in Sudoku

The primary trick for finding Y Wing is identifying your candidates in the first place. To hone this skill, become familiar with the patterns that show up in different boards. A good place to start is with these three classic Y Wing template boards. The first board in the middle illustrates the basic Y Wing concept with three pairs of candidates that interact with each other. The other boards show the complexity of the pattern as the boards progress.

You can get more used to finding Y Wing by practicing on these classic Sudoku boards. Here are three scenarios to get you started.

1. Classic Y-Wing Board
2. Pattern: Starting with the upper two 1s (r1c4 r3c6), the linked yellow example Y Wing basics. It eliminates all 6s in r2 and r3. Difficulty Level Very easy. Logic: Start by focusing on the corner r1c4 outside boxes. Note that r1c4 is the only place where a 1 can be entered into the entirety of the outside boxes. The same rule applies to r3c6 of the opposite corner to form the matching wing. Drawing the y wing then allows the 2, 3, 4, 5, 7, 8, and 9s in the middle box r2c5 and bottom box rc3c4 to be eliminated.
3. Classic Y-Wing Board
4. Pattern: A more complex example of a Y-Wing. Any 3s outside of the r4 or c1 box, are either an instant 3, or they form an instant 3. They will form the 3 in r5c6. Difficulty Level Easy. Logic The outside corners are the trickiest pieces of information to find first, so we will start with the central corner instead. Start by identifying one of corner pairs r4c9 (dark green). This corner only has one 3. The same rules apply to r5c1. The match requires a non-aligned r5. Draw in the Y-Wing then go to the top dark green corner to see where the elimination can be made. Noticing less frequently used numbers (in this case a 7) can make it easier to identify candidates and make it easier to identify the elimination.
5. Classic Y-Wing Board
6. Pattern: A complex setup for a twist on a classic basic Y-Wing. In row 6, all the 1s are eliminated. The twistis that the 2 is in one of the cells adjacent to the V point. Difficulty Level Very Easy. Logic: Look at number 2. The V point sees a 2 in c9 and an eliminate 2 in c8 and c9. If 9 is true, this is because of the single 2 in r6, c8. Draw in the Y Wing. The key to identifying this one is the V point seeing all 3 2s in that direction. Often, it may be helpful to look at the elimination points to see if the have a familiar pattern.

Tip 1: Practice Identifying Y Wing Patterns

Practice the Y Wing (aka Black Widow) strategy by solving expert level Sudoku puzzles until you are able to regularly and easily identify permutations of 123, 126, 129, 356, 359, and 789 representing Y Wings. Use logic and visualization to look for them across different groups of cells. The more you practice seeing and identifying the basic three-cell Y Wing pattern and the six value options that correlate with it, the quicker you will become at finding Y Wings and crossing off numbers as a result of them.

Tip 2: Look for Multiple Y Wing Patterns in a Puzzle

After finding a Y Wing pattern, it is worth looking for multiple Y Wing chains in the puzzle. An additional Y Wing chain can be created with a candidate number this is not in the pattern. Creating multiple Y Wing chains in a puzzle increases the likelihood that one will break open the puzzle and allow for more candidate removals.

Additionally, one may be able to use the Y Wing patterns in connection with each other in a puzzle. A double Y Wing pattern is when two Y Wing patterns are next to one another on the same candidate numbers B, G, F, at angle endpoints for candidate numbers F, G, B, or with horizontal or vertical bars for candidate number AG.

Extremely Hard Sudoku Puzzle #3 from WebSudoku has two angles endpoints with G (9) on all corners, and with M and D on all corners. This is indicated by the red ovals in the following image.

Tip 3: Use Pencil Marks to Keep Track of Elimination Possibilities

Y wing logic is one of many advanced solving techniques in sudoku that involves tracking multiple relationships between different candidate cells. As multiple candidate sequences are analyzed, the sudoku board can become cluttered with numerous possibilities.

To avoid confusion, mark candidate values or pencil marks in each cell. A pencil mark is simply the individual candidate number in a cell. Utilizing pencil marks to display possible Y wing patterns is a tried and true technique to keep track of choices, prevent forgetting or overlooking a potential Y wing, and make application of Y wing logic more efficient.

For example, pencil marks for a Y wing candidate can be filled in when two candidates with the same value could be part of a Y wing. In this case, if your board situation does not warrant applying Y wing logic or you establish that one of the candidates in the W or Z pair can be eliminated, you can easily erase that pencil mark and remove the segments for that candidate from your Y wing.

Frequently Asked Questions

How do you use the reference data to find the Y Wing in Sudoku?

To use the reference data, you will need to look for three squares that form the shape of a “y” in the puzzle. These three squares will have two numbers each, and the third number will be the same in all three squares. This forms the Y Wing pattern that can help you solve the puzzle.

What is the benefit of using the Y Wing technique in Sudoku?

The Y Wing technique is a powerful tool that can help you solve even the most challenging Sudoku puzzles. It allows you to eliminate possible number options in certain squares, making it easier to fill in the remaining numbers and complete the puzzle.

Can the Y Wing technique be used on any Sudoku puzzle?

Yes, the Y Wing technique can be used on any Sudoku puzzle. However, it is most effective on more difficult puzzles that require advanced solving techniques. It may not be necessary to use this technique on easier puzzles, where simpler methods can suffice.

Are there any variations of the Y Wing technique?

Yes, there are variations of the Y Wing technique that you can use to solve Sudoku puzzles. Some of these variations include the XY Wing, XYZ Wing, and W Wing. Each of these techniques follows a similar concept but with slight variations in the pattern formation.

Is the Y Wing technique difficult to learn?

The Y Wing technique may seem daunting at first, but with practice, it can become second nature. It is a popular technique among advanced Sudoku players and can be learned easily through tutorials and practice puzzles.

Can I use the Y Wing technique in combination with other solving techniques?

Yes, the Y Wing technique can be used in combination with other solving techniques, such as the Naked Pairs or Hidden Pairs methods. Combining these techniques can make it easier to solve even the most challenging Sudoku puzzles.