Y-Cycle (Discontinuous) is an advanced logic strategy similar to the XY-Cycle (Discontinuous) and XY-Chain. It involves checking a specific candidate in a specific cell to see if a chain of consequences leads to a contradiction.
If assuming "Cell A is 1" eventually proves that "Cell A is NOT 1," then the original assumption was impossible.
[!NOTE] Real Example Pending: This strategy is a specific variant of the XY-Cycle/Chain family. 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 "Contradiction Loop"
Imagine a chain of bivalue cells (cells with exactly 2 candidates) that loops back to the start:
- Start: Cell A {1, 2}. Assume A = 1.
- Link: Cell B {2, 3}. If A=1 → then ... (chain logic)
- Link: Cell C {3, 4}.
- ...
- Return: The chain eventually forces Cell A to be 2.
The Contradiction: - We started by assuming A = 1. - The logic proved that this leads to A = 2 (which means A ≠ 1). - Therefore, A cannot be 1. - Elimination: Remove 1 from Cell A.
Visual Guide
``` Step 1: Assume START is 1 [START] {1,2} = 1 (ON) ↓ [Cell B] {1,3} = 3 (Implied) ↓ [Cell C] {3,4} = 4 (Implied) ↓ [Cell D] {4,2} = 2 (Implied) ↓ [START] {1,2} = 2 (Implied) -> NOT 1 (OFF)
RESULT: Start=1 implies Start≠1. CONCLUSION: Start is NOT 1. ```
Why "Discontinuous"?
- Continuous Loop: All links represent "strong" relationships. You can start anywhere, go either direction, and it works perfectly.
- Discontinuous Loop: There is a "break" or a "weakness" in the logic that creates a specific contradiction at one point (the discontinuity).
In this case, the discontinuity is at the Start/End cell. The chain works fine everywhere else, but it "crashes" when it tries to reconnect to the start.
Comparison Table
| Strategy | Chain Components | Logic Type | Elimination |
|---|---|---|---|
| X-Cycle | Single Digit (Strong/Weak links) | Contradiction | Based on specific digit links |
| XY-Chain | Bivalue Cells | Endpoint Inference | At start/end only |
| Y-Cycle (Disc.) | Bivalue Cells | Self-Contradiction | At the starting cell itself |
How to Spot It
- Highlight Bivalue Cells: This strategy exclusively uses cells with 2 candidates.
- Pick a Start: Choose a bivalue cell and "test" one candidate mentally.
- Follow the Chain: Trace the forced implications (If this is A, that must be B...).
- Look for Return: Does the chain curve back to your starting cell?
- Check Result: If it returns as the opposite value, you found a Y-Cycle Discontinuous.
Tips for Beginners
- Don't Guess Randomly: Only follow forced moves (strong links). If a cell has 3 options, you can't assume which one is next.
- Use Coloring: Draw the chain physically or use a coloring tool.
- Parity Matters: These loops essentially check "Odd vs Even" steps. A conflict in parity creates the elimination.
Common Mistakes
- Assuming Continuity: Thinking "I found a loop!" means you can eliminate everywhere. Only Continuous loops allow outside eliminations. Discontinuous loops only allow checking the specific contradiction point.
- Broken Links: Using a cell with 3 candidates as a link. This breaks the "If A then B" certainty required for the chain.
Related Strategies
- XY-Cycle (Discontinuous): The broader category for this logic.
- XY-Chain: The linear version.