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2025-07-20T15:42:49Z

Created page with "'''Supercoloring''' is the precursor to Multi-Colors, which eventually evolved into Ultracoloring and 3D Medusa. This advanced solving technique was originally..."

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'''Supercoloring''' is the precursor to [[Multi-Colors]], which eventually evolved into [[Ultracoloring]] and [[3D Medusa]]. This advanced [[solving technique]] was originally designed for computer solvers, although it can be executed by a human solver with lots of paper and patience.

== How it Works ==

The technique operates on all remaining [[candidate]]s in the grid, excluding the [[given]]s and the solved [[cell]]s. Although it considers all remaining candidates, it is still a [[single-digit]] solving technique. Interactions between different [[digit]]s 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 pair]]s 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.

== External Links ==

* [http://www.setbb.com/sudoku/viewtopic.php?p=766#766 Introduction on Sudoku Programmers forum]

== See Also ==

* [[Coloring]]
* [[Multi-Colors]]
* [[Ultracoloring]]
* [[3D Medusa]]

[[Category:Solving Techniques]]

Supercoloring - Revision history

Rooted: Created page with "'''Supercoloring''' is the precursor to Multi-Colors, which eventually evolved into Ultracoloring and 3D Medusa. This advanced solving technique was originally..."