Platon Sudoku · Sudoku Study

Sashimi X-Wing · Step-by-step example

Two base rows or columns use two cover lines, but one corner is absent. An extra candidate acts as a fin beside the missing corner. Remove the digit only from a cover-line target that also sees the fin.

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Recognize the pattern

Two base rows or columns use two cover lines, but one corner is absent. An extra candidate acts as a fin beside the missing corner.

How to find it

Find three X-Wing corners and a fin on the base line with the missing corner, in the same box as that corner.

What it allows

Remove the digit only from a cover-line target that also sees the fin.

Avoid the mix-up

Three corners alone do not justify an elimination. Confirm the fin and check that the target sees it; do not mark the missing corner as a candidate.

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 · Recognize the degenerate X-Wing

The two base lines (row 6, row 8) and two cover lines (column 6, column 9) show the whole degenerate fish. For 2, R8C6=2 and R8C9=2 are the two ends of the strong pair in row 8. Across the other base row 6, R6C9=2 is the remaining body corner; R6C6 is the missing corner and has no candidate 2. Thus the body is R6C9=2, R8C6=2, R8C9=2, while R6C4=2 are fins in box 5. The targets R4C6=2, R5C6=2 lie on column 6 and see every fin.

Step 2 · Case 1: the end beside the missing corner is true

If the strong-pair end R8C6=2 is true, the other end R8C9=2 is false. Because R8C6=2 and the targets R4C6=2, R5C6=2 share column 6, every target is false in this case.

Step 3 · Case 2: the end beside the body corner is true

If the other strong-pair end R8C9=2 is true, R8C6=2 is false, and the aligned body corner R6C9=2 is false through column 9. The base row 6 must then place 2 in at least one fin among R6C4=2. Every target R4C6=2, R5C6=2 sees every fin, so every target is false in this case too.

Step 4 · The two cases cover every possibility

The strong pair in row 8 has exactly the two ends R8C6=2 and R8C9=2, so one of the two cases must occur. The first end directly excludes R4C6=2, R5C6=2; the second forces at least one fin, which also excludes R4C6=2, R5C6=2. These cases exhaust all placements, so remove the targets.

What it allows

Sashimi X-Wing · Remove the digit only from a cover-line target that also sees the fin.

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 · Recognize the degenerate X-Wing

The two base lines (column 1, column 5) and two cover lines (row 6, row 8) show the whole degenerate fish. For 8, R8C1=8 and R6C1=8 are the two ends of the strong pair in column 1. Across the other base column 5, R6C5=8 is the remaining body corner; R8C5 is the missing corner and has no candidate 8. Thus the body is R6C1=8, R6C5=8, R8C1=8, while R7C5=8 are fins in box 8. The targets R8C4=8 lie on row 8 and see every fin.

Step 2 · Case 1: the end beside the missing corner is true

If the strong-pair end R8C1=8 is true, the other end R6C1=8 is false. Because R8C1=8 and the targets R8C4=8 share row 8, every target is false in this case.

Step 3 · Case 2: the end beside the body corner is true

If the other strong-pair end R6C1=8 is true, R8C1=8 is false, and the aligned body corner R6C5=8 is false through row 6. The base column 5 must then place 8 in at least one fin among R7C5=8. Every target R8C4=8 sees every fin, so every target is false in this case too.

Step 4 · The two cases cover every possibility

The strong pair in column 1 has exactly the two ends R8C1=8 and R6C1=8, so one of the two cases must occur. The first end directly excludes R8C4=8; the second forces at least one fin, which also excludes R8C4=8. These cases exhaust all placements, so remove the targets.