Y-Cycle (Continuous) is nearly identical to the XY-Cycle (Continuous) strategy. It refers specifically to continuous loops formed by bivalue cells (cells with exactly 2 candidates).
In a continuous loop, every link is validated by the loop's structure. This means the connection between every pair of cells becomes a Strong Link—one of them must contain the linking value.
[!NOTE] Real Example Pending: This strategy is extremely rare. We are currently waiting for a pure example in our database. The following is a theoretical explanation.
Interactive Example
Click "Apply Logic" to see the strategy in action.
The Logic: The Bivalue Loop
Imagine a set of cells that form a perfect ring:
- Cell A {1, 2}
- Cell B {2, 3}
- Cell C {3, 1}
- Return: Cell C connects back to Cell A via '1'.
Trace it: - If A=1 → C=3 → B=2. (Valid) - If A=2 → B=3 → C=1. (Valid)
Both scenarios work perfectly. The loop "stabilizes" itself.
The Eliminations
Since the loop is stable, we know that for any link (e.g., the '2' connecting A and B): - Either A is 2, OR B is 2. - It is impossible for neither to be 2.
Therefore: Any cell outside the loop that "sees" both A and B cannot be a 2. We can eliminate 2 from all such peer cells.
Visual Guide
Row 1 Row 2
[A] {1,2} ═══ [B] {2,3} <- Link is '2'
║ │
║ │
[C] {3,1} ────┘
The double line (═══) represents a link that has become Strong because of the loop. - One of A or B must be 2. - Peers of A and B lose candidate 2.
Comparison Table
| Strategy | Cycle Type | Link Result | Elimination |
|---|---|---|---|
| XY-Chain | Open (No loop) | Inference | Start/End Only |
| Y-Cycle (Continuous) | Closed (Perfect) | Strong Links | Peers of Links |
| Y-Cycle (Discontinuous) | Closed (Broken) | Contradiction | Evaluation Cell |
How to Spot It
- Map Bivalue Cells: Find clusters of cells with only 2 candidates.
- Draw Chains: Connect them where they share a digit.
- Find a Ring: Look for a chain that comes back to the start.
- Check Edges: Does the last cell share a digit with the first? If yes, it's Continuous!
Tips for Beginners
- Short Loops: Most useful continuous loops are small (3-5 cells).
- Rectangles: A "Unique Rectangle" is actually a tiny continuous loop of length 4.
- Coloring: Use two colors to trace the ON/OFF state of the loop.
Common Mistakes
- Using Non-Bivalue Cells: A true Y-Cycle uses only bivalue cells. If you include a cell with 3 candidates, the logic is much weaker (unless you are using advanced AIC rules).
- Eliminating Inside: You usually eliminate from other cells, not the cells in the loop itself (unless a candidate inside the loop creates a contradiction).
Related Strategies
- XY-Cycle (Continuous): The same concept, often used interchangeably.
- XY-Chain: The open chain version.
- Unique Rectangle: A special case of a 4-cell loop.