sudokUI › Sudoku techniques › AIC with ALSs
AIC with ALSs in sudoku
An Alternating Inference Chain that uses an ALS as a strong link between two of its digits: if X is nowhere in the ALS, Y must be somewhere in it.
Why it works
Without X the ALS has N candidates for N cells, so all are placed, Y included. At least one end is true, eliminating candidates weakly linked to both: an ALS digit weakly links to that digit in outside cells seeing every ALS cell holding it.
How to spot it
A bivalue cell already gives a strong link, so look next at two cells in one unit holding three candidates between them.
Worked example
![AIC with ALSs example on a sudoku board. AIC with ALS: 8@r2c9 → 8@r2c8 → 8@[r7c8, r8c8] → 9@[r7c8, r8c8] → 9@r6c8 → 9@r6c9; at least one end is true, so candidates conflicting with both ends are removed.](/learn/img/aic-with-als.svg)
AIC with ALS: 8@r2c9 → 8@r2c8 → 8@[r7c8, r8c8] → 9@[r7c8, r8c8] → 9@r6c8 → 9@r6c9; at least one end is true, so candidates conflicting with both ends are removed.
Practise it on a real puzzle. sudokUI generates a puzzle that needs AIC with ALSs 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 AIC with ALSs, the puzzle's difficulty rating grows by 360. Its class is Unfair. It is needed in 1 in 590 puzzles that sudokUI generates. How the rating works.
More chains and loops
Remote Pair · Chute Remote Pair · X-Chain · X-Cycles (loops) · Grouped X-Cycles · XY-Chain · Twinned XY-Chains · Nice Loop · Grouped Nice Loop · Alternating Inference Chain · AIC with Groups