Techniques · Mental
Simple coloring
Pick a digit. Wherever that digit has exactly two homes in a house, those two cells are linked: one of them is the digit, the other isn't. Color the links alternately. Two colors cover the chain.
If two cells of the same color can see each other, that color is impossible, and every cell of that color loses the digit. A cell outside the chain that can see both colors loses the digit too, because one of the colors is real.
When it shows up
Simple coloring is a Mental technique. Mental puzzles are the ones whose hardest step is coloring or an XY-chain.
Coloring is beyond the NYT archive. None of the 1,483 puzzles needs a chain.
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 the 5s in this chain.