3D Medusa is a powerful extension of Simple Coloring. While Simple Coloring is restricted to a single digit, 3D Medusa connects different digits using Strong Links.
It builds a massive web of logical connections across the grid. We use two colors (e.g., Red and Blue) to track the state of these candidates.
[!NOTE] Real Example Pending: This strategy is an advanced AIC network technique. 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: Strong Links Only
3D Medusa relies entirely on Strong Links. A Strong Link exists when:
1. Bi-value Cell: A cell has exactly two candidates (e.g., {1, 2}). If it's not 1, it must be 2.
2. Bi-location Unit: A candidate appears exactly twice in a row, column, or box. If it's not in Spot A, it must be in Spot B.
We chain these links together, coloring them alternately: - Node A (Red) → Node B (Blue) → Node C (Red) → Node D (Blue)...
Elimination Types
Once the network is colored, we look for contradictions or logical eliminations. There are six standard rules, but these are the most common:
1. Two Colors in One Cell (Eliminate Color)
If a single cell ends up having two candidates of the same color (e.g., Candidate 1 is Red and Candidate 2 is Red), that color implies the cell has two values simultaneously. Impossible! - Result: All "Red" candidates are False. Eliminate them. All "Blue" candidates are True.
2. Two Colors in One Unit (Eliminate Color)
If a Row/Col/Box has two candidates of the same color for the same digit (e.g., two Red '5's in Row 1), that color is impossible. - Result: All "Red" candidates are False. Eliminate them.
3. Cell Sees Both Colors (Eliminate Candidate)
If an uncolored candidate "sees" a Red node and a Blue node of the same digit (or conflicting digits in a bivalue cell), it implies that candidate is impossible regardless of which color is true. - Result: Eliminate the uncolored candidate.
4. Same Color Sees Itself (Eliminate Candidate)
If a Red '5' sees another Red '5', then Red must be false. - Result: Eliminate all Red candidates.
Visual Guide
Cell A {1,2} Cell B {2,3}
(1=Red, 2=Blue) ─── (2=Red, 3=Blue)
│
│
Cell C {3,4}
(3=Red, 4=Blue)
Notice how the colors flip logic across digits: - If A is 1 (Red), then A is NOT 2. - If A is NOT 2, then B MUST be 2 (Red checks out). - Wait... B cannot be 2 if A is 1? - Correction: In 3D Medusa, linked nodes have Opposite colors. - A(1): Red - A(2): Blue - B(2): Red (Strong link with A(2)) - B(3): Blue
The coloring tracks "True/False" states.
Comparison Table
| Strategy | Scope | Link Types | Complexity |
|---|---|---|---|
| Simple Coloring | Single Digit | Strong Links | Medium |
| X-Cycle | Single Digit | Strong & Weak | High |
| XY-Chain | Multiple Digits | Bivalue Cells | High |
| 3D Medusa | Multiple Digits | All Strong Links | Very High |
Rules for Coloring
- Start: Pick a Strong Link (anywhere). Color one end Red, the other Blue.
- Expand: Propagate colors.
- If a cell has
Redcandidate, the other candidate in that bivalue cell becomesBlue. - If a unit has
Redcandidate, the other instance of that digit in the unit becomesBlue.
- If a cell has
- Check: Apply the elimination rules above.
Tips for Beginners
- Use Pencil Colors: This is impossible to do in your head. You need a tool that supports coloring candidates.
- Start Small: Look for clusters of bivalue cells first (XY-Chains), as they are naturally strong-linked.
- Don't Guess: Only color across Strong Links. If you cross a weak link, the logic breaks.
Related Strategies
- Simple Coloring: The basis for this strategy.
- XY-Chain: A subset of Medusa rules restricted to bivalue cells.