sudokUI › Sudoku techniques › X-Cycles (loops)
X-Cycles (loops) in sudoku
single-digit Nice Loop · how it fits
A closed loop of cells holding candidate X whose links alternate strong and weak throughout, or except at one cell where two strong or two weak links meet.
Why it works
In a fully alternating loop every weak link has X at one end, so X is removed from outside cells seeing both ends of one weak link. Two strong links meeting place X in that cell, and two weak links meeting remove X from it.
How to spot it
Draw the conjugate pairs of one digit, join them where cells see each other, and check whether the chain returns to its starting cell.
Implemented, but never needed: an easier technique always reaches the same result first.
In a puzzle's rating
Each time the solver needs X-Cycles (loops), the puzzle's difficulty rating grows by 280. Its class is Unfair. It is needed in fewer than 1 in 5,500,000 puzzles that sudokUI generates. How the rating works.
More chains and loops
Remote Pair · Chute Remote Pair · X-Chain · Grouped X-Cycles · XY-Chain · Twinned XY-Chains · Nice Loop · Grouped Nice Loop · Alternating Inference Chain · AIC with Groups · AIC with ALSs