3D Medusa Sudoku Coloring Explained

Build one connected color network

Begin with a strong link, a pair of candidates where one must be true. This can be a shape that has exactly two positions in a row, column, or box, or the two candidates inside a bivalue cell. Give one end color A and the other color B. Then keep propagating. Whenever a colored candidate has a strong link to an uncolored candidate, give the new candidate the opposite color. A bivalue cell can carry the color from one shape to another, while a conjugate pair can carry it to another cell. This is what makes the method three-dimensional: the network moves through rows, columns, boxes, cells, and multiple symbols instead of staying on one candidate value. In a Shapedoku grid, you might begin with a heart pair, pass through a heart-or-crescent cell, and continue along a crescent pair elsewhere. Accurate Notes are essential because one forgotten candidate can turn a supposed strong link into a false one.

Use contradictions to reject a color

The two colors represent opposite truth states throughout the connected network. If one color creates an impossible situation, every candidate carrying that color is false and the opposite color is true. The clearest contradiction occurs when two candidates of the same color represent the same shape and see each other in one row, column, or box. Both cannot be true, so that color fails. Another contradiction occurs when one cell contains two candidates of the same color. A cell can hold only one shape, yet the color state would make both true, so that color must be false. When you find either pattern, do not apply the conclusion immediately. Trace the network back and verify each strong link. The power of 3D Medusa comes from propagation, but that same reach means one incorrect link can contaminate many cells. A short, verified network is more valuable than an impressive web you cannot explain.

Find eliminations that see both colors

A color network can also remove candidates without proving either color globally. Suppose an uncolored heart candidate sees a color A heart and also sees a color B heart. One of those colored hearts must be true, so the uncolored candidate cannot survive. The two colored hearts do not need to see each other; the target simply needs to see both. A similar idea works inside a cell. If an uncolored candidate shares a cell with one colored candidate and sees an opposite-colored version of itself through a unit, inspect the exact implications before eliminating. Beginners should stay with the safest rule: an outside candidate for one shape that sees both colors of that same shape can be removed. After every elimination, leave coloring mode and rescan for singles, pairs, and locked candidates. On an Extreme Shapedoku puzzle, one Medusa elimination is often enough to collapse a difficult region without coloring the entire board.

• Use only verified strong links: conjugate pairs or bivalue cells.
• Alternate colors every time you cross a strong link.
• Reject a color if it places the same shape twice in one unit.
• Reject a color if it makes two candidates true in one cell.
• Remove an uncolored candidate that sees both colors of the same shape.
• Stop after a useful result and return to simpler techniques.