AIC Sudoku: Alternating Inference Chains for Expert Solvers (2026)

An AIC (Alternating Inference Chain) connects candidate positions (often written as (d)rNcN) with links that strictly alternate strong and weak. When the endpoints share a digit and “see” a target cell, you earn an elimination; when the chain closes as a loop with correct parity, you can collect loop rules that go beyond a single endpoint pair.

This page is the narrow intent treatment: one proof technology, one notation habit, one decision rule for when to stop naming fish and start chaining.

Pattern

• Strong link: if one endpoint candidate is false, the other must be true (conjugate pair in a unit, or a bivalue cell’s two candidates treated carefully).
• Weak link: two candidates share a unit; they cannot both be true.

The chain must alternate S–W–S–W… (or the dual formulation your primer uses—consistency matters more than dialect). AIC sudoku work is mostly parity bookkeeping: a “shortcut” chain is usually a broken alternation or a weak link pretending to be strong.

Logic

Reach for an AIC when:

• Fish and wings are exhausted or only give near-miss geometry.
• A digit’s conjugate graph is busy, but the elimination you need is multi-house and does not name itself as X-Wing.
• You can keep the chain short enough to audit; if the sketch spans half the grid before the first conclusion, try ALS-XZ or a digit-only cycle first.

AIC generalizes many named moves: a clean X-Wing is a short single-digit AIC; many forcing chains are two-branch stories about the same implication graph. For binary branch proofs, compare forcing chains.

Example (compact Eureka fragment)

A readable fragment might look like:

(3)r5c5 = (3)r5c8 - (7)r5c8 = (7)r7c8

Read it left to right as alternating inferences: each = is strong, each - is weak, and the chain continues only while every step is licensed in the current candidate state. If you cannot justify the next link aloud, stop—that is where guesses masquerade as chains.

Pitfalls

• Broken alternation after you add a group node or compress several cells—re-expand and re-label.
• Weak links between non-peers in the same digit line (classic visibility error).
• Over-long chains when an ALS-XZ or X-Cycle would have been the shorter certificate.

Where to go next

• Single-digit specialization: X-Cycles in Sudoku.
• Set-based unlocks before you chain: ALS-XZ.
• Full sequencing and case narrative: how to solve extreme Sudoku.

When you want technique-scoped hints and stable pencil marks while you train parity, practice on rated boards in Sudoku Face Off—or read how we frame teaching hints for advanced work on Sudoku app advanced hints (2026).