X-Cycles

Expert

Strong and weak links for a single digit form cycles; nice loops enable eliminations or placements.

How It Works

For a single digit, build a chain using "strong links" (a unit where the digit is only in two cells) and "weak links" (cells in the same unit). If the chain forms a continuous nice loop, candidates at the weak link positions can be eliminated. Discontinuous loops reveal contradictions, enabling placements or eliminations.

Example

4
58
36
91
58
2
36
7
15
2
36
4
56
7
136
89
7
18
923
68
16
45
261
58
58
3974
874192
36
5
36
395674812
56
35
27
68
149
368
169
13
7
38
4
69
52
1368
169
48
35
2
59
7
36
136
Key cells of the techniqueCells where elimination is appliedCandidate to be placedEliminated candidate (crossed out)

Practice with a Real Puzzle

This 9×9 puzzle is solver-verified to require this technique on its solution path.

Hard24 givensStrict