An XY-Chain walks through bi-value cells. Each step shares a digit with the next, like stepping stones labeled with two letters each. It is another special AIC.
Why it works
If you start and end with the same digit D on the chain ends, then D cannot be false at both ends — the chain would contradict itself.
So at least one end is D. Any cell that sees both ends cannot be D.
How to spot it
Only walk through bi-value cells. Matching end digit is the sting.
Demonstration
Find a path of bi-value cells that starts and ends with the same digit.
The green cells form an XY-Chain. The shared end digit is 9.
Both ends cannot be false for 9. At least one end is 9 — check both worlds along the path.
Eliminate 9 from cells that see both ends (red).
Example 1
Walk a bi-value chain with matching end digits.
This XY-Chain eliminates 6.
Remove 6 from cells that see both ends (red). At least one end must be that digit.
Example 2
Walk a bi-value chain with matching end digits.
This XY-Chain eliminates 8.
Remove 8 from cells that see both ends (red). At least one end must be that digit.