Platon Sudoku · Sudoku Study

XYZ-Wing · Step-by-step example

A three-candidate pivot {X,Y,Z} sees two two-candidate wings {X,Z} and {Y,Z}. Remove Z only from a cell that sees the pivot and both wings.

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Recognize the pattern

A three-candidate pivot {X,Y,Z} sees two two-candidate wings {X,Z} and {Y,Z}.

How to find it

Find a three-candidate cell and two wings that each retain Z plus a different other pivot digit.

What it allows

Remove Z only from a cell that sees the pivot and both wings.

Avoid the mix-up

This is stricter than XY-Wing: a target seeing only the wings may still be valid. Check all three sight lines.

Step-by-step example · Row link

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 · Find the pivot and wings

R5C9 is the three-candidate pivot 2, 7, 9. It sees the two wings: R5C4 with 2, 9, and R6C9 with 2, 7. Together they form an XYZ-Wing.

Step 2 · Find the target shared by all three

The pivot and both wings contain 2. Every target (R5C8=2) sees all three possible locations of 2.

Step 3 · Case 1: R5C9 is 7

If R5C9=7, R6C9 cannot be 7 and must be 2. Every target (R5C8=2) sees the current 2 in R6C9, so remove candidate 2 from those targets.

Step 4 · Case 2: R5C9 is 9

If R5C9=9, R5C4 cannot be 9 and must be 2. Every target (R5C8=2) sees the current 2 in R5C4, so remove candidate 2 from those targets.

Step 5 · Case 3: the pivot is 2

If R5C9=2, the pivot itself already supplies 2. This is the third and final pivot value. Every target (R5C8=2) sees the current 2 in the pivot, so remove candidate 2 from those targets.

Step 6 · Combine the three cases

For every possible pivot value, one of R5C4, R5C9, R6C9 is 2. Every target sees all three cells, so remove R5C8=2.

What it allows

For every possible pivot value, one of R5C4, R5C9, R6C9 is 2. Every target sees all three cells, so remove R5C8=2.

XYZ-Wing · Remove Z only from a cell that sees the pivot and both wings.

Step-by-step example · Column link

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 · Find the pivot and wings

R6C5 is the three-candidate pivot 4, 5, 7. It sees the two wings: R6C4 with 4, 5, and R8C5 with 4, 7. Together they form an XYZ-Wing.

Step 2 · Find the target shared by all three

The pivot and both wings contain 4. Every target (R4C5=4) sees all three possible locations of 4.

Step 3 · Case 1: R6C5 is 5

If R6C5=5, R6C4 cannot be 5 and must be 4. Every target (R4C5=4) sees the current 4 in R6C4, so remove candidate 4 from those targets.

Step 4 · Case 2: R6C5 is 7

If R6C5=7, R8C5 cannot be 7 and must be 4. Every target (R4C5=4) sees the current 4 in R8C5, so remove candidate 4 from those targets.

Step 5 · Case 3: the pivot is 4

If R6C5=4, the pivot itself already supplies 4. This is the third and final pivot value. Every target (R4C5=4) sees the current 4 in the pivot, so remove candidate 4 from those targets.