sudokUI › Sudoku techniques › Alternating Inference Chain

Alternating Inference Chain in sudoku

umbrella over X- and XY-Chains · how it fits

Unfair · rating cost 320 · Chains and Loops · also called AIC

A chain of candidates, which may mix digits, whose links alternate strong, weak, strong and so on, beginning and ending with a strong link.

Why it works

If one end is false the links force the other true, so at least one end is true. Any candidate weakly linked to both ends is eliminated, whether through a shared cell or through the same digit in cells that see each other.

How to spot it

Conjugate pairs and bivalue cells give the strong links: join them where two candidates share a cell, or share a digit and a unit.

Worked example

Alternating Inference Chain example on a sudoku board. AIC: 8@r1c6 → 4@r1c6 → 4@r5c6 → 2@r5c6 → 2@r5c9 → 2@r1c9; at least one of 8@r1c6 and 2@r1c9 is true, so candidates conflicting with both are removed. — remove the chain

AIC: 8@r1c6 → 4@r1c6 → 4@r5c6 → 2@r5c6 → 2@r5c9 → 2@r1c9; at least one of 8@r1c6 and 2@r1c9 is true, so candidates conflicting with both are removed.

Step 28 of this puzzle's solution, found and verified by the sudokUI engine. Cells are named by row and column: r2c3 is row 2, column 3. Play this puzzle from the start.

Practise it on a real puzzle. sudokUI generates a puzzle that needs Alternating Inference Chain and takes you straight to the position where it applies. Hints draw the pattern on the board and explain the step.

Practice Alternating Inference Chain Open in the app's guide

In a puzzle's rating

Each time the solver needs Alternating Inference Chain, the puzzle's difficulty rating grows by 320. Its class is Unfair. It is needed in 1 in 190 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 · AIC with Groups · AIC with ALSs

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