Simple 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.
Learn the technique3D 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.
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 build a network of linked candidates, just as in Simple Coloring. This time the network stretches across multiple different digits, not just one.
- The links are of two kinds: two cells that are the only two places a digit can go in a row, column or box, or the two candidates in one and the same cell, since only one of them can be true.
- We color the network every other link, blue and orange. One color must be true in the final solution.
- Look at the cross-marked candidates. Each of them is blocked by both colors, either through a neighbor with the same digit or through another colored candidate in its own cell.
- No matter which color is true, these candidates cannot be true, so we remove them.
How to recognize the pattern
3D Medusa is coloring in multiple dimensions. Where Simple Coloring only links cells for one digit, Medusa also links the two candidates inside a cell with exactly two candidates. Such two-valued cells act as bridges between digits, and the result is one large network of candidates in two colors.
The colors share fate across digits: either all blue candidates are correct, or all orange. If you find a contradiction in one color, for example the same digit twice in the same unit or two colors in the same cell with the same digit, that whole color is wrong, and all candidates with that color can be removed. Without contradiction, you can still remove candidates that are blocked by both colors.
Step-by-step procedure
- Start like in Simple Coloring with one digit and a strong link, and give the two candidates each their color.
- Expand the network through all strong links, and use two-valued cells to jump between digits: if a cell has only two candidates, they get opposite colors.
- Look for a contradiction in one of the colors. If you find one, remove all candidates of that color and place the opposite color.
- If you find no contradiction, remove candidates that see a colored candidate of the same digit and at the same time share a cell with the other color.
Common mistakes
- Jumping between digits via cells with three candidates. The bridge between two digits requires a cell with exactly two candidates.
- Treating colors as fact. A color is a hypothesis, and without a contradiction you do not know which one is correct.
- Losing a coloring step. The network grows quickly, so write down the colors in the candidate notes instead of keeping them in your head.
When do you need the technique?
Puzzles at Extreme level require techniques that combine three or more cells in logical reasoning of the if-then type. Try your way through the examples below, step by step, using the same tools the solver uses on your own 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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