The XY-Chain is effectively a giant Y-Wing.
Where a Y-Wing has just 3 cells (Pivot + 2 Wings), an XY-Chain can have any number of cells (4, 5, 6, etc.), but follows the exact same "domino" logic.
It relies entirely on bivalue cells (cells with exactly two candidates).
Interactive Example
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Click "Apply Logic" to see the strategy in action.
Real Example Explanation
In the example above, we want to prove that either the Start or the End of our chain is a 2.
- The Chain:
- Start: R4C7 has candidates {2, 9}. (If it's not 2, it's 9).
- Link 1: R4C7 (9) connects to R6C9 {9, 5}. (If R4C7 is 9, R6C9 is 5).
- Link 2: R6C9 (5) connects to R9C9 {5, 8}. (If R6C9 is 5, R9C9 is 8).
- End: R9C9 (8) connects to R8C7 {8, 2}. (If R9C9 is 8, R8C7 is 2).
- The Logic:
- Trace the path: If the Start is NOT 2 -> then ... -> then ... -> the End MUST be 2.
- Result: It is impossible for both ends to be "not 2". One of them holds the 2.
- The Elimination:
- Any cell that can see BOTH the Start (R4C7) and the End (R8C7) cannot be a 2.
- Since both are in Column 7, all other empty cells in that column can eliminate 2.
How to Spot It
- Find Bivalue Cells: Locate cells with exactly two candidates.
- Build a Chain: Connect them like dominoes.
- Cell A {1, 2} connects to Cell B {2, 3} (via the 2).
- Cell B {2, 3} connects to Cell C {3, 4} (via the 3).
- And so on...
- Check the Ends:
- The Start cell must have your target number (e.g., 1).
- The End cell must also have your target number (e.g., 1).
- Eliminate: Remove the target number from the "Kill Zone" (intersection of Start and End).
Comparison
- Y-Wing: An XY-Chain with length 3.
- Remote Pairs: An XY-Chain where every cell has the same pair of numbers.
- XY-Chain: Can mix and match pairs (e.g., {1,2} -> {2,3} -> {3,5} -> {5,1}).