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Platon Sudoku · Sudoku Study

Finned X-Wing · Step-by-step example

An X-Wing has an extra candidate in one base row or column. The fin lies in the same box as a base corner. Remove the digit only where the target shares a cover column with the X-Wing and sees the fin in its box.

This course is adapted from Platon Sudoku App. Read the complete example here, then continue learning and practising in the app.

View on Google Play

Recognize the pattern

An X-Wing has an extra candidate in one base row or column. The fin lies in the same box as a base corner.

How to find it

Find two base rows and two cover columns, then look for an extra candidate beside one corner in its box.

What it allows

Remove the digit only where the target shares a cover column with the X-Wing and sees the fin in its box.

Avoid the mix-up

Do not clear the entire cover column. The target must see the fin; verify all base candidates and the shared box.

Step-by-step example · Row

This example starts from a saved intermediate position. Its candidates include earlier logical eliminations; they are not fresh automatic notes.

Blue: evidence. Green: conclusion. Crossed-out digits: eliminated candidates. R1C1 means row 1, column 1.

Step 1 · Build the complete fish body

For 9, the two base lines (row 5, row 7) and two cover lines (column 3, column 5) define the four body candidates R5C3=9, R5C5=9, R7C3=9, R7C5=9. The extra candidates R7C4=9 are fins in box 8. The targets R8C5=9, R9C5=9 lie in a cover line outside the base lines.

For 9, the two base lines (row 5, row 7) and two cover lines (column 3, column 5) define the four body candidates R5C3=9, R5C5=9, R7C3=9, R7C5=9. The extra candidates R7C4=9 are fins in box 8. The targets R8C5=9, R9C5=9 lie in a cover line outside the base lines.
For 9, the two base lines (row 5, row 7) and two cover lines (column 3, column 5) define the four body candidates R5C3=9, R5C5=9, R7C3=9, R7C5=9. The extra candidates R7C4=9 are fins in box 8. The targets R8C5=9, R9C5=9 lie in a cover line outside the base lines.
Step 2 · Separate the fins from the body

The outlined candidates R7C4=9 are the fins in box 8; the other four candidates R5C3=9, R5C5=9, R7C3=9, R7C5=9 are the X-Wing body. Now check both possibilities: a fin is true, or every fin is false.

The outlined candidates R7C4=9 are the fins in box 8; the other four candidates R5C3=9, R5C5=9, R7C3=9, R7C5=9 are the X-Wing body. Now check both possibilities: a fin is true, or every fin is false.
The outlined candidates R7C4=9 are the fins in box 8; the other four candidates R5C3=9, R5C5=9, R7C3=9, R7C5=9 are the X-Wing body. Now check both possibilities: a fin is true, or every fin is false.
Step 3 · Assume fin 1 is true

If the fin R7C4=9 is true, every marked target R8C5=9, R9C5=9 sees it in box 8, so those targets cannot be 9.

If the fin R7C4=9 is true, every marked target R8C5=9, R9C5=9 sees it in box 8, so those targets cannot be 9.
If the fin R7C4=9 is true, every marked target R8C5=9, R9C5=9 sees it in box 8, so those targets cannot be 9.
Step 4 · Case: every fin is false

If every fin R7C4=9 is false, the four body candidates R5C3=9, R5C5=9, R7C3=9, R7C5=9 form an ordinary X-Wing across the two base lines (row 5, row 7) and two cover lines (column 3, column 5). The targets R8C5=9, R9C5=9 lie in a cover outside the bases, so the X-Wing excludes them.

If every fin R7C4=9 is false, the four body candidates R5C3=9, R5C5=9, R7C3=9, R7C5=9 form an ordinary X-Wing across the two base lines (row 5, row 7) and two cover lines (column 3, column 5). The targets R8C5=9, R9C5=9 lie in a cover outside the bases, so the X-Wing excludes them.
If every fin R7C4=9 is false, the four body candidates R5C3=9, R5C5=9, R7C3=9, R7C5=9 form an ordinary X-Wing across the two base lines (row 5, row 7) and two cover lines (column 3, column 5). The targets R8C5=9, R9C5=9 lie in a cover outside the bases, so the X-Wing excludes them.
Step 5 · Apply both target conditions

A valid target must satisfy both conditions: it lies in an X-Wing cover outside the two bases, and it sees every fin. The targets R8C5=9, R9C5=9 satisfy both, so remove candidate 9.

A valid target must satisfy both conditions: it lies in an X-Wing cover outside the two bases, and it sees every fin. The targets R8C5=9, R9C5=9 satisfy both, so remove candidate 9.
A valid target must satisfy both conditions: it lies in an X-Wing cover outside the two bases, and it sees every fin. The targets R8C5=9, R9C5=9 satisfy both, so remove candidate 9.

What it allows

A valid target must satisfy both conditions: it lies in an X-Wing cover outside the two bases, and it sees every fin. The targets R8C5=9, R9C5=9 satisfy both, so remove candidate 9.

Finned X-Wing · Remove the digit only where the target shares a cover column with the X-Wing and sees the fin in its box.
Finned X-Wing · Remove the digit only where the target shares a cover column with the X-Wing and sees the fin in its box.

Step-by-step example · Column

This example starts from a saved intermediate position. Its candidates include earlier logical eliminations; they are not fresh automatic notes.

Blue: evidence. Green: conclusion. Crossed-out digits: eliminated candidates. R1C1 means row 1, column 1.

Step 1 · Build the complete fish body

For 5, the two base lines (column 2, column 9) and two cover lines (row 1, row 5) define the four body candidates R1C2=5, R1C9=5, R5C2=5, R5C9=5. The extra candidates R6C2=5 are fins in box 4. The targets R5C1=5 lie in a cover line outside the base lines.

For 5, the two base lines (column 2, column 9) and two cover lines (row 1, row 5) define the four body candidates R1C2=5, R1C9=5, R5C2=5, R5C9=5. The extra candidates R6C2=5 are fins in box 4. The targets R5C1=5 lie in a cover line outside the base lines.
For 5, the two base lines (column 2, column 9) and two cover lines (row 1, row 5) define the four body candidates R1C2=5, R1C9=5, R5C2=5, R5C9=5. The extra candidates R6C2=5 are fins in box 4. The targets R5C1=5 lie in a cover line outside the base lines.
Step 2 · Separate the fins from the body

The outlined candidates R6C2=5 are the fins in box 4; the other four candidates R1C2=5, R1C9=5, R5C2=5, R5C9=5 are the X-Wing body. Now check both possibilities: a fin is true, or every fin is false.

The outlined candidates R6C2=5 are the fins in box 4; the other four candidates R1C2=5, R1C9=5, R5C2=5, R5C9=5 are the X-Wing body. Now check both possibilities: a fin is true, or every fin is false.
The outlined candidates R6C2=5 are the fins in box 4; the other four candidates R1C2=5, R1C9=5, R5C2=5, R5C9=5 are the X-Wing body. Now check both possibilities: a fin is true, or every fin is false.
Step 3 · Assume fin 1 is true

If the fin R6C2=5 is true, every marked target R5C1=5 sees it in box 4, so those targets cannot be 5.

If the fin R6C2=5 is true, every marked target R5C1=5 sees it in box 4, so those targets cannot be 5.
If the fin R6C2=5 is true, every marked target R5C1=5 sees it in box 4, so those targets cannot be 5.
Step 4 · Case: every fin is false

If every fin R6C2=5 is false, the four body candidates R1C2=5, R1C9=5, R5C2=5, R5C9=5 form an ordinary X-Wing across the two base lines (column 2, column 9) and two cover lines (row 1, row 5). The targets R5C1=5 lie in a cover outside the bases, so the X-Wing excludes them.

If every fin R6C2=5 is false, the four body candidates R1C2=5, R1C9=5, R5C2=5, R5C9=5 form an ordinary X-Wing across the two base lines (column 2, column 9) and two cover lines (row 1, row 5). The targets R5C1=5 lie in a cover outside the bases, so the X-Wing excludes them.
If every fin R6C2=5 is false, the four body candidates R1C2=5, R1C9=5, R5C2=5, R5C9=5 form an ordinary X-Wing across the two base lines (column 2, column 9) and two cover lines (row 1, row 5). The targets R5C1=5 lie in a cover outside the bases, so the X-Wing excludes them.
Step 5 · Apply both target conditions

A valid target must satisfy both conditions: it lies in an X-Wing cover outside the two bases, and it sees every fin. The targets R5C1=5 satisfy both, so remove candidate 5.

A valid target must satisfy both conditions: it lies in an X-Wing cover outside the two bases, and it sees every fin. The targets R5C1=5 satisfy both, so remove candidate 5.
A valid target must satisfy both conditions: it lies in an X-Wing cover outside the two bases, and it sees every fin. The targets R5C1=5 satisfy both, so remove candidate 5.

What it allows

A valid target must satisfy both conditions: it lies in an X-Wing cover outside the two bases, and it sees every fin. The targets R5C1=5 satisfy both, so remove candidate 5.

Finned X-Wing · Remove the digit only where the target shares a cover column with the X-Wing and sees the fin in its box.
Finned X-Wing · Remove the digit only where the target shares a cover column with the X-Wing and sees the fin in its box.

Practice

This course is adapted from Platon Sudoku App. Read the complete example here, then continue learning and practising in the app.

View on Google Play