Peak Sudoku
Fish, wings, chains & uniquenessPeak Score 75–90

Nice Loop (AIC)

An alternating chain of strong and weak links – open or closed.

Also known as: Alternating Inference Chain, AIC, Continuous Loop, Discontinuous Loop

Quick Summary

An Alternating Inference Chain alternates strong links (if false, must be true) and weak links (cannot both be true). It generalizes wings, fish, and chains into a unified deductive system.

Understanding the Nice Loop (AIC) Technique

Alternating Inference Chains (AICs), historically called Nice Loops, represent the unifying theory of advanced Sudoku deductions. An AIC alternates between strong links (where a candidate is forced if the previous is false) and weak links (where two candidates cannot both be true). An open chain that starts and ends with strong links on a target candidate proves that at least one endpoint must be that digit, clearing it from all cells seeing both ends. A closed continuous loop turns every weak link into a strong link, triggering widespread eliminations across the entire loop.

Visual Examples

Green cells highlight the Nice Loop (AIC) pattern, amber cells denote where candidates are affected, and struck-through pencil marks show the eliminations. Use the buttons or arrow keys to browse examples.

Example 1 of 5
Chain: R3C1=2 ≡ R3C1=7 – R1C1=7 ≡ R1C6=7 – R1C6=2 ≡ R3C6=2 ≡ means one of the two ends must be true - either that cell is down to just those two digits, or that digit fits in only those two cells of a row, column, or box. – means the two ends can't both be true - either they are two digits in one cell, or the same digit in two cells that share a row, column, or box. Because the chain can't be broken, one of its two endpoints (R3C1=2 or R3C6=2) must hold its digit. Any other cell that sees both endpoints is therefore impossible for that digit - it gets removed either way.
Removes: 2 from R3C3, R3C9

How to Spot & Solve a Nice Loop (AIC) (Step-by-Step Guide)

The complete visual scanning and logical deduction process to execute this technique:

  • 1Identify alternating strong links (if false, must be true) and weak links (cannot both be true) across candidates or cells.
  • 2Follow the alternating path: a strong link guarantees a candidate, which weakly eliminates a neighbor, which strongly forces the next candidate.
  • 3If the chain starts and ends with strong links on the same digit in two different cells, at least one endpoint must hold that digit.
  • 4Eliminate that digit from any cell that sees both endpoints of an open chain.
  • 5If the chain closes into a continuous loop, every weak link along the cycle is promoted into a strong exclusion, triggering eliminations around the loop.

Common Traps & Mistakes to Avoid

  • Having two consecutive weak links or two consecutive strong links without valid grouped nodes.
  • Treating a weak link as strong (assuming that because a candidate is false, another must be true when it wasn't the only option).
  • Misreading candidate eliminations at the endpoints.

Frequently Asked Questions

What is the difference between an open AIC and a closed Nice Loop?

An open AIC has two distinct endpoints and eliminates candidates seeing both ends. A closed Nice Loop connects back to its starting cell, allowing eliminations at every weak link around the cycle.

Expand your repertoire by learning prerequisites and advanced counterparts:

XY-ChainPeak Score 70–85

A chain of bivalue cells that forces a digit at both endpoints.

Read guide →
ALS ChainPeak Score 80–95

Links built from almost-locked sets – N cells sharing N+1 candidates.

Read guide →
Forcing ChainPeak Score 90–100

Both branches from a bivalue cell reach the same conclusion.

Read guide →

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