sudokUI › Sudoku techniques › Nice Loop
Nice Loop in sudoku
an AIC written as a loop · how it fits
A loop of candidates whose links alternate strong and weak, either perfectly all the way round or everywhere except at one candidate where two strong or two weak links meet.
Why it works
With perfect alternation one end of every weak link is true: if both ends share a cell its other candidates go, otherwise their digit leaves cells seeing both. A candidate where two strong links meet is placed, one where two weak links meet is eliminated.
How to spot it
Follow alternating links out from a bivalue cell or conjugate pair and watch for the chain returning to link with its starting candidate.
Worked example
Nice Loop: the continuous loop 3@r1c4 → 4@r1c4 → 4@r6c4 → 4@r6c5 → 3@r6c5 → 3@r2c5 alternates perfectly; every weak link has exactly one true side, clearing other candidates along it. So 2 is removed from r6c5; 3 is removed from r2c4, r2c6; 4 is removed from r3c4, r8c4.
Practise it on a real puzzle. sudokUI generates a puzzle that needs Nice Loop and takes you straight to the position where it applies. Hints draw the pattern on the board and explain the step.
In a puzzle's rating
Each time the solver needs Nice Loop, the puzzle's difficulty rating grows by 280. Its class is Unfair. It is needed in 1 in 25 puzzles that sudokUI generates. How the rating works.
More chains and loops
Remote Pair · Chute Remote Pair · X-Chain · X-Cycles (loops) · Grouped X-Cycles · XY-Chain · Twinned XY-Chains · Grouped Nice Loop · Alternating Inference Chain · AIC with Groups · AIC with ALSs