Techniques · Mental
XY-chain
An XY-chain is a path of cells that each have two candidates. Each cell shares one candidate with the next cell, and the two cells see each other, so they can't both be that shared digit. The chain starts and ends on the same digit.
One of the ends is that digit. Any other cell that sees both ends loses it. An XY-wing is the short chain: a pivot and two wings. A longer path is the same argument.
When it shows up
XY-chains are Mental, with simple coloring. They are the hardest step this solver uses.
The NYT archive never needs an XY-chain. Medium stops at pointing, and Hard stops at triples.
See it on a real puzzle
The marks are the candidates left when this is the next step in the solve. Step through it: the pattern, what leaves, and what that forces.
See the pattern
Look at this chain of pairs.