How it Works

The technique operates on all remaining candidates in the grid, excluding the givens and the solved cells. Although it considers all remaining candidates, it is still a single-digit solving technique. Interactions between different digits are not taken into consideration.

Assign Colors

Each remaining candidate receives a different color. For practical purposes, letters are used to represent these colors. In this stage, conjugate pairs are ignored. A grid with 50 remaining candidates will have 50 different colors.

Build Exclusion Matrix

Create a list of all color pairs which are mutually exclusive, because they represent the same digit in a single house. You only need half the matrix. A excludes B also implies B excludes A.

Build Conjugate Matrix

Create a list of all color pairs which form a conjugate pair in one or more houses.

Recolor Equivalent Colors

When A is conjugate to B and A is conjugate to C, B and C are equivalent. Every C is replaced by B in the results. This process is repeated until no more colors can be merged. At the end, each pair of conjugate colors represents a color cluster.

Build Implication Matrix

Using the Exclusion Matrix and the Conjugate Matrix, a third matrix is calculated. The following rule is used:

When A excludes B and B is conjugate to C, A implies C. This matrix only works in a single direction. When A implies C, it is not true that C also implies A.

Evaluate the Results

The Contradiction rule
When A implies B and A implies C and B excludes C, we have found a contradiction, allowing us to eliminate the candidates for color A.
The Identity rule
When A implies B and B implies A, A and B are equivalent and we can replace all instances of B by A. After this recoloring, we may be able to expand the Exclusion Matrix.

Supercoloring and other Coloring Techniques

Supercoloring did not survive as a solving technique, but its remnants can be found in Multi-Colors and other coloring techniques. Although these techniques use the same principles, the process is simplified so it can be performed by human solvers.

Sudoku Games

Free Sudoku Script for Your Website

Sudoku strategies

Printable Sudoku

Sudoku Links

sudoku cool sudoku schwer sudoku gratuit sudoku gratis 数独 数独 Судоку онлайн бесплатно 数独 今日数独 武士数独