LeafyOrbSudoku techniques · Expert level
X-Wing: how to spot it and use it
An X-Wing uses one digit that has exactly two possible cells in each of two rows, and those cells sit in the same two columns. The digit must take opposite corners of that rectangle, so it can be removed from every other cell in those two columns. It works the same with columns and rows swapped.
How it works
Picture the four cells as the corners of a rectangle. In the top row, the digit goes in the left or the right corner. Whichever it is, the bottom row must take the other side, because a column cannot hold the digit twice. So the digit sits on one diagonal or the other: that is the X.
Both diagonals put one copy of the digit in each of the two columns. So those columns already have their digit from these two rows, and every other cell in the two columns can lose it.
X-Wings are where Sudoku moves past single boxes and lines, which is why Ninebloom first needs one at the Expert level.
- The row, column or box the move uses
- The cells that make the pattern
- Candidates the move removes
Example 1 · Row · from Expert puzzle #556
The 1 can go in row 4 only in R4C3 and R4C7, and in row 7 only in R7C3 and R7C7. The four cells make a rectangle on columns 3 and 7. The two rows must place their 1s on opposite corners, so either way column 3 and column 7 get their 1 from these rows. Remove 1 from R5C3, R6C3, R1C7 and R8C7.
NG-16NZLG-4Y1G3M-ASL62F-GBYX0V-IK9LM6-JYS1JK-9PNGHR-4CYXKY-P9OGQ
Cells are named by row and column: R4C3 is row 4, column 3. Boxes are numbered 1 to 9, left to right and top to bottom.
How to spot it
- Clear all the singles and pairs first, and fill in pencil marks.
- Pick one digit at a time. Do not hunt for "any" X-Wing.
- Find rows where that digit has exactly two candidates.
- Look for two such rows whose candidates are in the same two columns.
- Remove the digit from the rest of those two columns. Then try columns as the base instead of rows.
More examples
Example 2 · Column · from Expert puzzle #209
The 4 can go in column 3 only in R4C3 and R8C3, and in column 8 only in R4C8 and R8C8. The four cells make a rectangle on rows 4 and 8. The two columns must place their 4s on opposite corners, so either way row 4 and row 8 get their 4 from these columns. Remove 4 from R8C1, R8C6, R8C7 and R8C9.
NG-187ZUR-HTOZ55-U2A3B3-0O4TBV-XM628X-03HIT6-VRPRHJ-BQ30AS-WPAGA
Example 3 · Row · from Expert puzzle #629
The 5 can go in row 1 only in R1C3 and R1C9, and in row 7 only in R7C3 and R7C9. The four cells make a rectangle on columns 3 and 9. The two rows must place their 5s on opposite corners, so either way column 3 and column 9 get their 5 from these rows. Remove 5 from R2C3, R2C9 and R8C9.
NG-1ARU74-P012L6-YFT2AT-5JDL65-F1J4SQ-YL9UOU-IN35WT-9YOB4V-DYIHQ
Common mistakes
- A row with three candidates for the digit. Each of the two base rows needs exactly two.
- Removing from the rows. With rows as the base, the eliminations are in the columns, and the other way round.
- Corners in different columns. All four cells must share just two columns.
Questions
Why is it called an X-Wing?
The two ways the digit can fall are the two diagonals of the rectangle, which together look like an X.
What is the difference between an X-Wing and a Swordfish?
A Swordfish is the same idea across three rows and three columns instead of two. An X-Wing is the smallest of these "fish" patterns.
Can an X-Wing use columns instead of rows?
Yes. If a digit has exactly two places in each of two columns, in the same two rows, remove it from the rest of those rows. The second example above is a column X-Wing.
Which Ninebloom level needs an X-Wing?
Expert. A puzzle is rated Expert when it cannot be solved without an X-Wing, and Fiendish puzzles need moves beyond it.