Windoku · Extreme

XY-Wing in Windoku

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

The idea

An XY-Wing is a pivot {X, Y} and two wings it sees, {X, Z} and {Y, Z}. One wing must be Z, so a cell that sees both wings cannot be Z.

In Windoku a pivot and a wing can see each other through a window, even when they share no row, column or box.

Worked examples

2 positions from real Windoku 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

R1C3 (teal) has just two candidates: 4 and 6.

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

A wing linked by a window

Extreme puzzle · XY-Wing

One wing shares no row, column or box with the pivot. The lit window is what links them.

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 Windoku puzzles are the first to need it.

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

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

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

The worked examples, every step

Pivot and wings

Extreme Windoku puzzle · XY-Wing

  1. R1C3 (teal) has just two candidates: 4 and 6.
  2. It sees two cells (green): R1C6 with {4, 9} and R5C3 with {6, 9}. If the pivot is 4, R1C6 becomes 9; if it is 6, R5C3 does. Either way one green cell is 9.
  3. A cell that sees both green cells cannot be 9. Eliminate 9 from R5C6.
  4. Done: 9 is eliminated from R5C6.

A wing linked by a window

Extreme Windoku puzzle · XY-Wing

  1. One wing shares no row, column or box with the pivot. The lit window is what links them.
  2. R7C6 (teal) has just two candidates: 1 and 8.
  3. It sees two cells (green): R8C5 with {1, 5} and R6C8 with {5, 8}. If the pivot is 1, R8C5 becomes 5; if it is 8, R6C8 does. Either way one green cell is 5.
  4. A cell that sees both green cells cannot be 5. Eliminate 5 from R8C8.
  5. Done: 5 is eliminated from R8C8.

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