Peak Sudoku

Nice Loop (AIC)

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

Tier 4
Fish, wings, chains & uniqueness
Typical difficulty
Peak Score 75–90
Also known as
Alternating Inference Chain, AIC, Continuous Loop, Discontinuous Loop

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.

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.

Worked examples

1 / 5
Reading the exampleCells forming the patternCells losing candidatesEliminated candidates

Suppose R3C1 is not 2.

  1. Then R3C1 is 7, since only 2 and 7 are left there.
  2. So R1C1 is not 7, since column 1 holds just one 7.
  3. So R1C6 is 7, since row 1 has nowhere else for 7.
  4. So R1C6 is not 2, since a cell holds just one digit.
  5. So R3C6 is 2, since column 6 has nowhere else for 2.

Either R3C1 or R3C6 is 2, so 2 can be removed from any cell that sees both.

Removes: 2 from R3C3, R3C9

How to apply it

Spotting the pattern and making the deduction, in order.

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

  • 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.
Peak Score 70–85XY-ChainA chain of bivalue cells that forces a digit at both endpoints.Peak Score 80–95ALS ChainLinks built from almost-locked sets – N cells sharing N+1 candidates.Peak Score 90–100Forcing ChainBoth branches from a bivalue cell reach the same conclusion.

Put Nice Loop (AIC) into practice

Try a puzzle from the Extreme tier (Peak Score 81–90).

Play a Extreme puzzleAll 25 techniques