Alternating chain
MasterAn alternating chain mixes the X-chain and the XY-chain. Its links join candidates: strong ones (two places for a digit in a unit, or two digits in a cell) and weak ones (candidates that can’t both be true). Alternating them from a strong link to a strong link proves one end or the other is true.
How to spot it
- Start from a strong link: a digit with two places in a unit, or a cell with two candidates.
- Alternate weak and strong links, moving between digits and cells as you go.
- With strong links at both ends, remove what sees both end candidates.
Why it works
Each strong link says that if one end is false, the other is true; each weak link says that if one end is true, the other is false. Chained, they say that if the first candidate is false, the last one is true.
Example
5
3
1
4
8
7
3
8
5
6
5
9
1
3
2
4
5
6
5
1
5
1
8
9
2
6
3
7
5
3
5
7
8
7
5
6
1
9
2
3
Follow the highlighted chain.
Common mistakes
- Treating a weak link as strong: two cells that see each other can both be empty of the digit.
- Losing track of which digit a link is about when the chain changes digits inside a cell.