XY-Wing
XY-Wing uses three bivalue cells (pivot + two wings) to force an elimination in shared-visibility cells.
Checklist
- Find a pivot with two candidates (X,Y).
- Find two wings linked as (X,Z) and (Y,Z).
- Locate cells seeing both wings.
- Remove Z from those shared-visibility cells.
Place in the Learning Course
Treat this page as a lesson, not only a reference. Check the condition, solve one matching puzzle, then review which candidate or cell made the step valid.
1. Find it
Run the checklist in order until you can explain the pattern.
2. Verify it
Compare the valid and invalid diagrams before removing candidates.
3. Practice it
Open the linked difficulty archive and look for the same condition.
Valid pattern: pivot-wing structure closes
The linked pattern forces Z in one wing branch, so shared cells cannot keep Z.
Valid pivot-wing chain with a forced elimination.
Invalid pattern: missing visibility condition
If a target cell cannot see both wings, Z elimination is not justified.
Visibility gap invalidates elimination.
Avoid applying it too early
Use this technique only when every checklist condition is true. A board can look similar while still missing one required limit, and removing a candidate too early can break the puzzle later. Before you act, say which unit, which digit, and which cells make the move valid.
- Fix the row, column, or box you are reasoning about before removing candidates.
- Separate candidates that can be removed from candidates that must remain.
- After the removal, rescan for naked singles or hidden singles created by the update.
How to test it in a real puzzle
After reading the article, do not immediately jump to a harder level. Open one linked difficulty archive and look for the same condition while the checklist is still visible. If the pattern does not appear, that is still useful: write down which row, column, box, digit, or candidate set you checked. That note makes the next related technique easier to choose.
Where to use this
Primarily Hard and Expert.
Read next
After-Puzzle Review
- Write down one cell or candidate affected by this technique.
- Check whether you almost removed a candidate without the full condition.
- Choose whether to solve one more puzzle at this level or read the related technique first.