Alternating Inference Chains (AIC)

Extreme

The most general chain technique — alternating strong and weak links; both endpoints' common candidate is eliminated from cells seeing both ends.

How It Works

AIC is the most general chain form in Sudoku solving. Chains alternate between strong links (one of two cells must have the digit) and weak links (both cells can't both have the digit).

Rule: If both ends of the chain share a common candidate, any cell seeing both ends can have that candidate eliminated. If the chain loops, further inferences apply.

Many techniques (X-Cycles, XY-Chain, W-Wing) are special cases of AIC.

Example

17
35
6
24
8
27
9
24
3
29
4
38
26
15
16
27
5
18
38
7
15
9
13
25
14
26
46
5
16
7
38
4
19
13
28
26
14
29
24
16
7
49
8
13
15
48
16
18
37
25
3
27
49
19
6
25
29
4
19
17
13
8
37
47
38
45
17
16
79
6
14
25
7
19
14
5
26
8
24
13
29
Key cells of the techniqueCells where elimination is appliedCandidate to be placedEliminated candidate (crossed out)

Chain: R1C3=4 — R1C3≠7 = R5C3 — ... = R5C8-3. Cells seeing both start and end nodes have the common candidate eliminated.

Practice with a Real Puzzle

This 9×9 puzzle is solver-verified to require this technique on its solution path.

Hard26 givensStrict