Jigsaw · Extreme

XY-Wing in Jigsaw Sudoku

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 Jigsaw a pivot and a wing can see each other through their region, even when they share no row or column.

Worked examples

2 positions from real Jigsaw 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

R3C1 (teal) has just two candidates: 6 and 9.

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

A wing linked by its region

Extreme puzzle · XY-Wing

One wing shares no row or column with the pivot. The lit region 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 Jigsaw puzzles are the first to need it.

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

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

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

The worked examples, every step

Pivot and wings

Extreme Jigsaw puzzle · XY-Wing

  1. R3C1 (teal) has just two candidates: 6 and 9.
  2. It sees two cells (green): R3C3 with {1, 6} and R8C1 with {1, 9}. If the pivot is 6, R3C3 becomes 1; if it is 9, R8C1 does. Either way one green cell is 1.
  3. A cell that sees both green cells cannot be 1. Eliminate 1 from R5C1, R7C3.
  4. Done: 1 is eliminated from R5C1, R7C3.

A wing linked by its region

Extreme Jigsaw puzzle · XY-Wing

  1. One wing shares no row or column with the pivot. The lit region is what links them.
  2. R5C8 (teal) has just two candidates: 3 and 4.
  3. It sees two cells (green): R5C2 with {3, 9} and R6C9 with {4, 9}. If the pivot is 3, R5C2 becomes 9; if it is 4, R6C9 does. Either way one green cell is 9.
  4. A cell that sees both green cells cannot be 9. Eliminate 9 from R6C2.
  5. Done: 9 is eliminated from R6C2.

Previous: X-Wing · Next: Swordfish