Nice Loop
A closed alternating chain that proves a candidate false, true, or impossible outside the loop.
What it is
A Nice Loop is an Alternating Inference Chain that returns to its starting candidate. The closing relationship determines the result. If the same candidate meets two weak links, it cannot be true and is removed. If it meets two strong links, it must be true. A continuous loop has no break at its start; it can still eliminate an outside candidate that sees both ends of one weak link. Each conclusion is local, visible, and checked from the current pencil marks.
How to spot it
Trace a sequence of candidates with alternating strong and weak links until it closes. Do not repeat a candidate before the loop closes. For a weak discontinuity, the start candidate is joined by weak links on both sides and can be crossed out. For a continuous loop, look outside the loop only at cells that see both ends of a weak same-digit link.
Worked example
Step through the reasoning below. Each step adds one layer: first the position, then the pattern, then the candidates involved, and finally what can be eliminated.
Step 1 of 4: The starting position
- Pattern cells
- 4/3, 4/7, 5/1, 7/1, 7/7
- Digits
- 5
- Eliminations
- 4/7
Press a marked square to point it out on the board above.
Why it matters
Nice Loops turn a difficult-looking chain into a finite proof you can follow one link at a time. They expose eliminations that pairs, fish and wings miss, without guessing. The interactive board and hint mode draw strong links solid and weak links dashed, so the closing argument stays readable on every screen.
Practise now
Solve a puzzle where this technique decides the game
Frequently asked questions
What makes a Nice Loop different from an AIC?
An AIC normally ends at two distinct candidates. A Nice Loop closes back on its starting candidate. That closure creates an extra conclusion: a weak or strong discontinuity decides the start candidate, while a continuous loop can remove a candidate outside the loop.
What is a weak discontinuity?
It means the same candidate has a weak link arriving from both directions. Both ends cannot be true together, so the starting candidate itself is impossible and can be eliminated. The lesson example uses exactly this safe conclusion.
Does a Nice Loop ever guess?
No. Sudoku Luna rebuilds every strong and weak link from the current candidate state. The step is accepted only when the loop closes with the right alternation and the complete consequence is verified.
Put it to use
Where you will meet it
Expert grids are the only place this pattern regularly decides the solve. Bring your notes.
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Type the position into the solver and it walks the whole solution, naming the technique behind every step — including this one.
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