sudokUI › Sudoku techniques › Grouped X-Cycles
Grouped X-Cycles in sudoku
single-digit Grouped Nice Loop · how it fits
An X-Cycle loop where a group of two or three X candidates in one box and one row or column acts as one cell, true if any member is X.
Why it works
Seeing a group means seeing every member. A fully alternating loop removes X from outside cells seeing both ends of a weak link, an end joining two strong links is true, so cells seeing it lose X, and one joining two weak links loses X.
How to spot it
Look for a unit whose X candidates all lie in a group plus one other cell or group: those two ends are strongly linked.
Worked example
Grouped X-Cycle on 2: a continuous loop through 6 nodes (groups included); along each weak link one side is 2, so 2 falls from outside cells seeing both sides. So 2 is removed from r3c6, r4c1, r3c1.
Practise it on a real puzzle. sudokUI generates a puzzle that needs Grouped X-Cycles 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 Grouped X-Cycles, the puzzle's difficulty rating grows by 300. Its class is Unfair. It is needed in 1 in 430 puzzles that sudokUI generates. How the rating works.
More chains and loops
Remote Pair · Chute Remote Pair · X-Chain · X-Cycles (loops) · XY-Chain · Twinned XY-Chains · Nice Loop · Grouped Nice Loop · Alternating Inference Chain · AIC with Groups · AIC with ALSs