X-Cycles

X-Cycles are chains of strong and weak links for a single digit that form loops. Depending on link arrangement, eliminations or placements can be determined.

Technique

1. Build a chain using strong links (exactly 2 in unit) and weak links (more than 2 in unit).
2. Even loop (alternating strong-weak): Eliminate the candidate from cells seeing two chain cells.
3. Odd loop with two strong links adjacent: The candidate between them must be true.
4. Odd loop with two weak links adjacent: The candidate between them must be false.

Tips

• X-Cycles generalize Skyscrapers, X-Wings, and other single-digit patterns.
• Strong links force truth; weak links force falsehood.
• Even loops confirm the chain; odd loops find contradictions.