Monkeymore Sudoku

X-Cycles

Level 10 · Brown Belt

Prerequisite: Single-Digit ChainsLearn next → Simple ColoringLearn next → AICLearn next → Forcing ChainsLearn next → Grouped X-Cycles

Overview

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.

How It Works

  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.

Example

Build an X-Cycle for digit 6 by following alternating strong and weak links.

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Tips & Patterns

  • 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.