3D Medusa
3D Medusa is coloring in multiple dimensions: the chains link both cells with the same digit and the two candidates inside the same cell.
Learn the techniqueSimple Coloring
Simple Coloring follows a chain of cells linked in pairs for one specific digit and colors every other cell. One color must be correct, and that can be used to eliminate candidates.
See the technique in practice
Work through the examples step by step. Each step explains what you see on the puzzle and why the conclusion holds.
Example:
- We follow digit 3. In some rows, columns and boxes there are only two cells left that can take 3. Such cells form pairs: if one cell does not get the digit, the other must.
- Several of the pairs share cells, so they hang together in a chain. Think of the chain as light switches linked together: flip one switch and all the others flip at the same time.
- We color every other cell in the chain blue and orange. Now there are only two possibilities: either all the blue cells get digit 3, or all the orange ones do.
- Look at the cross-marked cell in row 3, column 7. It sees both a blue and an orange cell in its own row, column or box.
- One color wins regardless, so digit 3 is guaranteed to land in a cell that this one sees. Then the cell itself cannot have 3, and we remove it from the notes.
How to recognize the pattern
Simple Coloring is used on one digit at a time. Look for units where the digit has only two possible placements, because the two cells form a strongly linked pair: if one cell is wrong, the other must be right. When such pairs are chained together, you can color every other cell with two colors.
All cells with the same color share the same fate: either all are correct, or all are wrong. This gives two conclusions. If two cells of the same color see each other, that color is impossible, and the digit can be removed from all cells of that color. And a cell outside the chain that sees both colors can never take the digit, because one of the colors will be right anyway.
Step-by-step procedure
- Choose a digit and mark all units where the digit has only two possible placements.
- Start in one of the cells and give it a color, give its partner in the same unit the opposite color, and continue along all strong links.
- Check if two cells of the same color see each other. If so, remove the digit from all cells of that color.
- Otherwise check if any cells outside the chain see both colors, and remove the digit there.
Common mistakes
- Linking via units with three or more possibilities. The chain requires strong links, that is, units where the digit has only two possible cells.
- Mixing colors mid-chain. One color mistake gives false conclusions, so be careful to alternate color with each jump.
- Removing from the chain itself without a conflict. Without a color conflict, only cells that see both colors can be removed.
When do you need the technique?
At Hard level you must see multiple units in context: digits that form rectangles across multiple rows, chains of linked cells and boxes that lock each other. The techniques still only remove candidates, but these are exactly the eliminations that open up the puzzle.
Try it on your own puzzle
Enter your puzzle in the Sudoku Solver and it will find the next step and explain the technique behind it.
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