Sudoku X Wing
X Wing
Take a look at row number 2 and row number 4 in this puzzle.Let's see which cells can contain the digit 8 in those two rows, they are highlighted in red.
It happens to be that those 4 cells (2 in each row) align up perfectly in the same two columns - column 5 and column 7.
This is called an X Wing.
These 4 cells form a shape of an X or a rectangle.
Rows number 2 and 4 are called base sets and the digit 8 is called fish digit.
There are more possible 8's in columns 5 and 7.
They highlighted in grey and we'll get back to them later.
Let's look back at rows R2 and R4 - there are only two possible ways for 8 to reside in those two rows.
Both are in opposite corners of the X Wing.
Option 1: If R2C5 is an 8 then neither R4C5 nor R2C7 can be an 8 (basic rule of Sudoku).
Therefor R4C7 must be an 8.
Option 2 is the other way round.
If R4C5 Is 8 than R2C7 must also be an 8.
Either way, if we look at column 5 it must have an 8 on R2C5 or R4C5.
Therefor we can eliminate 8 from all other cells in this column - R5C5 in particular.
Same thing with column 7 - it must have an 8 on R2C7 or R4C7.
Therefor we can eliminate 8 from all other cells in this column - R3C7.
This is what X Wing is about, eliminating candidates using logic.
Here is another example of X Wing.
Rows 6 and 9 are the base sets.
3 is the fish digit.
The possible cells for 3 in these rows are aligned up perfectly in the same two columns - column 4 and column 8.
They form an X Wing.
We can therefore eliminate 3 from all other cells in those 2 columns as you can see in the picture.
X Wing can also appear where the base sets are in column.
In the following example - columns 5 and 7 are the base sets.
3 is the fish digit.
The possible cells for 3 in these columns are aligned up perfectly in the same two rows - row 2 and row 7.
They form an X Wing.
We can therefore eliminate 3 from all other cells in those 2 rows as you can see in the picture:
How to find X Wings
Locating x wing is not very difficult once you have pencil marks in your Sudoku.
You should scan rows and columns for each digit and find a set of two rows or columns that align-up perfectly together.
Can you find the X Wing with the base of 8 in this puzzle?
The base rows are R4 and R9.
They are the only possible cells for 8 in rows 4 and 9 and they align up in the same columns.
End of Lesson
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Solving Techniques - Hidden Pairs
