AIC

Level 12 · Black Belt

Strategy:

Multi-Digit Chains

Requires:

X-CyclesXY-Chain

Overview

Alternating Inference Chain (AIC) is a powerful chain technique that links candidates through alternating strong and weak inferences, potentially spanning multiple digits. When a chain forms a loop or returns to its start, eliminations or placements follow.

How It Works

  1. Build a chain alternating strong links (conjugate pairs or bivalue cells) and weak links (shared houses).
  2. Type 1 (Continuous Loop): All cells in the chain form an even loop, allowing eliminations from cells seeing both ends of any strong link.
  3. Type 2 (Same cell, different digits): Both endpoints reach the same cell with different digits on strong links; all other candidates are eliminated from that cell.
  4. Type 3 (Discontinuous): Both endpoints have the same digit on strong links pointing at the same cell; that digit is eliminated from the start cell.

Example

Look for AIC.

1

AIC

Found an Alternating Inference Chain (AIC) of 6 nodes from r1c1 to r7c2.

2

AIC

The chain alternates strong and weak inferences: strong means at least one endpoint is true, weak means both cannot be true.

3

AIC

Both endpoints r1c1 and r7c2 have candidate 1 on strong links, so one of them must contain it.

4

AIC

Any highlighted cell that sees both endpoints cannot keep 1, because one endpoint must contain it.

5

AIC

Remove 1 from cells seeing both endpoints: r9c1.

6

Result after applying the technique.

Tips & Patterns

  • AIC generalizes many simpler techniques: X-Chains, XY-Chains, and remote pairs are all special cases.
  • Strong links can be within a house (conjugate pair) or within a cell (bivalue).
  • Practice with shorter chains before attempting longer ones.