sudokUI › Sudoku techniques › ALS-XY-Chain
ALS-XY-Chain in sudoku
XY-Chain made of sets · how it fits
Four almost locked sets form a chain: neighbours share a joining digit whose cells all see each other, each middle set's joins differ, and both ends hold another digit Z.
Why it works
If one end lacks Z it locks and places its joining digit, removing that digit from the next set, and so on until the far end must place Z. So Z is removed from any cell outside the chain seeing every Z in both ends.
How to spot it
Build the chain from small sets such as bivalue cells, link by link, and after three links check whether both ends share a candidate.
Worked example
ALS-XY-Chain: r4c2, r4c7 –9– r1c7 –3– r1c5, r1c6 –9– r7c5; digit 4 falls from cells seeing every 4 of both end sets. So 4 is removed from r4c5.
Practise it on a real puzzle. sudokUI generates a puzzle that needs ALS-XY-Chain and takes you straight to the position where it applies. Hints draw the pattern on the board and explain the step.
In a puzzle's rating
Each time the solver needs ALS-XY-Chain, the puzzle's difficulty rating grows by 340. Its class is Unfair. It is needed in 1 in 98 puzzles that sudokUI generates. How the rating works.