Proven Sudoku
Alternating Inference Chain
Also called AIC, Alternating Inference Chains, Nice Loop (open form).
New to this shorthand? How to read a sudoku grid explains r4c7, houses, candidates and the rest.
What it means
A chain that switches between two kinds of step. One step says at least one of these is true. The next says these cannot both be true. Alternate them and the two ends of the chain tell you something certain.
The exact rule, for stronger players
The rule, stated exactly: A sequence of nodes joined by alternating strong and weak inferences, beginning and ending with a strong inference. A node is a candidate, a group of candidates in one house, or an almost-locked set. If the two endpoints are both candidates of digit d, d is eliminated from every cell seeing both.
What it removes: With both endpoints on digit d, remove d from cells seeing both. With endpoints in one cell, that cell takes one of the two endpoint digits. Continuous loops additionally eliminate on every weak link in the loop.
Why it works: A strong inference between P and Q means at least one holds. A weak inference means at most one holds. Alternating them forces at least one endpoint to be true: assume the first endpoint false, and the alternation propagates a forced truth along the chain to the other end. Anything contradicted by both endpoints is therefore impossible.
Worked examples
None yet. This pattern does not turn up in our daily boards, so there is no real example to show. We would rather wait than draw a fake one.
Learn these first
Related chains
- Bowman's BingoPick a digit, assume it, and write out everything that follows until you either finish or hit a contradiction.
- Cell Forcing ChainTake one square and try each number it could hold.
- Continuous Nice LoopA loop where the reasoning closes back on itself with no weak spot.
- Digit Forcing ChainTake one number in one square.
- Discontinuous Nice LoopA loop that almost closes but has one weak spot.
How often does it come up?
Our rough estimate: the central technique of hard solving. Most named Tier 4 and Tier 5 patterns are short AICs, which is why the AIC restatement appears on every one of those pages.