sudokUI › Sudoku techniques › AIC with Groups
AIC with Groups in sudoku
An Alternating Inference Chain with at least one group node: two or three cells holding candidate X in one box and one row or column, true if any becomes X.
Why it works
A group and another X node are strongly linked when together they are a unit's only places for X, weakly linked when all their cells see each other. At least one chain end is true, so any candidate weakly linked to both ends is eliminated.
How to spot it
When a chain stalls at a unit with three places for X, check whether two of them form a group, restoring a strong link.
Worked example
![AIC with Groups example on a sudoku board. Grouped AIC: 6@r1c1 → 2@r1c1 → 2@[r3c2, r3c3] → 2@r3c6 → 2@r4c6 → 6@r4c6; at least one end is true, so candidates conflicting with both ends are removed. So 6 is removed from r4c1.](/learn/img/aic-with-groups.svg)
Grouped AIC: 6@r1c1 → 2@r1c1 → 2@[r3c2, r3c3] → 2@r3c6 → 2@r4c6 → 6@r4c6; at least one end is true, so candidates conflicting with both ends are removed. So 6 is removed from r4c1.
Practise it on a real puzzle. sudokUI generates a puzzle that needs AIC with Groups 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 Groups, the puzzle's difficulty rating grows by 340. Its class is Unfair. It is needed in 1 in 1,100 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 ALSs