Sudoku X · Extreme

XY-Wing in Sudoku X

A two-candidate pivot and two wings: whichever digit the pivot takes, one wing holds the third digit.

The idea

An XY-Wing is three cells with two candidates each: a pivot {X, Y} and two wings it sees, {X, Z} and {Y, Z}. Either way the pivot goes, one wing becomes Z, so a cell that sees both wings cannot be Z.

In Sudoku X the cells can see each other along a diagonal, which makes wings that do not exist in Classic.

Worked examples

2 positions from real Sudoku X puzzles on this site, the familiar case first. Step through each one: the board lights what each step talks about, and the arrows show what rules what out.

Pivot and wings

Extreme puzzle · XY-Wing

R7C3 (teal) has just two candidates: 5 and 8.

Step 1 of 4Step 2 of 4Step 3 of 4Step 4 of 4

A wing linked by the diagonal

Extreme puzzle · XY-Wing

One wing shares no row, column or box with the pivot. They see each other only along the lit diagonal.

Step 1 of 5Step 2 of 5Step 3 of 5Step 4 of 5Step 5 of 5

Where it fits

ExtremeXY-Wing is an Extreme technique: Extreme Sudoku X puzzles are the first to need it.

The Classic XY-Wing lesson teaches it on a plain 9×9 board. The Sudoku X overview explains the rule and the levels.

XY-Wing in the other styles: Jigsaw, Thermo, Windoku, Arrow.

Try it on an Extreme Sudoku X puzzle. Next Step points it out when it is the move.

The worked examples, every step

Pivot and wings

Extreme Sudoku X puzzle · XY-Wing

  1. R7C3 (teal) has just two candidates: 5 and 8.
  2. It sees two cells (green): R7C6 with {2, 5} and R7C7 with {2, 8}. If the pivot is 5, R7C6 becomes 2; if it is 8, R7C7 does. Either way one green cell is 2.
  3. A cell that sees both green cells cannot be 2. Eliminate 2 from R6C6. R6C6 sees R7C7 along the main diagonal.
  4. Done: 2 is eliminated from R6C6.

A wing linked by the diagonal

Extreme Sudoku X puzzle · XY-Wing

  1. One wing shares no row, column or box with the pivot. They see each other only along the lit diagonal.
  2. R2C2 (teal) has just two candidates: 4 and 7.
  3. It sees two cells (green): R7C7 with {3, 4} and R3C3 with {3, 7}. If the pivot is 4, R7C7 becomes 3; if it is 7, R3C3 does. Either way one green cell is 3. One of these links runs along the main diagonal.
  4. A cell that sees both green cells cannot be 3. Eliminate 3 from R3C7.
  5. Done: 3 is eliminated from R3C7.

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