X-Wing

Level 5 · Orange Belt

Strategy:

Requires:

Locked Candidates

Learn after:

Finned X-Wing Simple Coloring Skyscraper Swordfish Two-String Kite

Overview

X-Wing is a fish pattern using two rows and two columns. When a candidate appears in exactly two cells in two different rows, and these four cells share the same two columns, the candidate can be eliminated from other cells in those columns.

How It Works

Find a candidate that appears in exactly two cells in a row.
Find another row where the same candidate appears in exactly two cells in the same columns.
These four cells form a rectangle. The candidate must be in two diagonal corners.
Eliminate the candidate from other cells in those two columns.

Example

Starting position

Look for X-Wing.

Sudoku grid showing the initial puzzle state for Look for X-Wing.

1

Scan base columns 4 and 8 for 3

Base columns: 4 and 8. Check where digit 3 can appear in those columns.

Sudoku grid illustrating step 1: Scan base columns 4 and 8 for 3 — Base columns: 4 and 8. Check where digit 3 can appear in those columns.

2

r1c4 is already filled

r1c4 is already filled with 4.

Sudoku grid illustrating step 2: r1c4 is already filled — r1c4 is already filled with 4.

3

3 is blocked from r3c4 by the row

Digit 3 cannot go in r3c4 because r3c2 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 3: 3 is blocked from r3c4 by the row — Digit 3 cannot go in r3c4 because r3c2 is already in this row. Remove the entry or choose a different digit.

4

r4c4 is already filled

r4c4 is already filled with 9.

Sudoku grid illustrating step 4: r4c4 is already filled — r4c4 is already filled with 9.

5

3 is blocked from r6c4 by the row

Digit 3 cannot go in r6c4 because r6c1 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 5: 3 is blocked from r6c4 by the row — Digit 3 cannot go in r6c4 because r6c1 is already in this row. Remove the entry or choose a different digit.

6

r7c4 is already filled

r7c4 is already filled with 2.

Sudoku grid illustrating step 6: r7c4 is already filled — r7c4 is already filled with 2.

7

3 is blocked from r8c4 by the row

Digit 3 cannot go in r8c4 because r8c5 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 7: 3 is blocked from r8c4 by the row — Digit 3 cannot go in r8c4 because r8c5 is already in this row. Remove the entry or choose a different digit.

8

3 is blocked from r9c4 by row and box

Digit 3 cannot go in r9c4 because r9c3 is in this row and r8c5 is in this box. Remove the entry or choose a different digit.

Sudoku grid illustrating step 8: 3 is blocked from r9c4 by row and box — Digit 3 cannot go in r9c4 because r9c3 is in this row and r8c5 is in this box. Remove the entry or choose a different digit.

9

r1c8 is already filled

r1c8 is already filled with 6.

Sudoku grid illustrating step 9: r1c8 is already filled — r1c8 is already filled with 6.

10

r3c8 is already filled

r3c8 is already filled with 1.

Sudoku grid illustrating step 10: r3c8 is already filled — r3c8 is already filled with 1.

11

r4c8 is already filled

r4c8 is already filled with 4.

Sudoku grid illustrating step 11: r4c8 is already filled — r4c8 is already filled with 4.

12

r6c8 is already filled

r6c8 is already filled with 9.

Sudoku grid illustrating step 12: r6c8 is already filled — r6c8 is already filled with 9.

13

r7c8 is already filled

r7c8 is already filled with 7.

Sudoku grid illustrating step 13: r7c8 is already filled — r7c8 is already filled with 7.

14

3 is blocked from r8c8 by the row

Digit 3 cannot go in r8c8 because r8c5 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 14: 3 is blocked from r8c8 by the row — Digit 3 cannot go in r8c8 because r8c5 is already in this row. Remove the entry or choose a different digit.

15

3 is blocked from r9c8 by the row

Digit 3 cannot go in r9c8 because r9c3 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 15: 3 is blocked from r9c8 by the row — Digit 3 cannot go in r9c8 because r9c3 is already in this row. Remove the entry or choose a different digit.

16

3 is confined to rows 2 and 5

In each of these 2 columns, digit 3 is confined to the same 2 cover rows: 2 and 5.

Sudoku grid illustrating step 16: 3 is confined to rows 2 and 5 — In each of these 2 columns, digit 3 is confined to the same 2 cover rows: 2 and 5.

17

The pattern forms a X-Wing

That forms a X-Wing: the cover rows must hold the digit for the base columns, so other columns cannot keep it there.

Sudoku grid illustrating step 17: The pattern forms a X-Wing — That forms a X-Wing: the cover rows must hold the digit for the base columns, so other columns cannot keep it there.

18

Extra 3 candidates in rows 2 and 5

These are the extra 3 candidates in rows 2 and 5 that must be removed: r2c6, r5c6, r5c7 and r5c9.

Sudoku grid illustrating step 18: Extra 3 candidates in rows 2 and 5 — These are the extra 3 candidates in rows 2 and 5 that must be removed: r2c6, r5c6, r5c7 and r5c9.

19

Remove 3 from rows 2 and 5

Remove 3 from the extra cells in rows 2 and 5: r2c6, r5c6, r5c7 and r5c9.

Sudoku grid illustrating step 19: Remove 3 from rows 2 and 5 — Remove 3 from the extra cells in rows 2 and 5: r2c6, r5c6, r5c7 and r5c9.

20

Result

Result after applying the technique.

Sudoku grid showing the result after applying the technique

Tips & Patterns

X-Wings work on rows (eliminating from columns) or columns (eliminating from rows).
Look for candidates with exactly 2 occurrences per row/column.
The pattern forms a rectangle - visualize the 'X' shape.