The New Sudoku Players' Forum

[tso]

Does someone want to take a crack at explaining for *non-programming human solvers* -- to whatever degree they *can* be explained -- the variously named coloring tactics? Maybe with some easy-to-follow diagrams?

I understand simple coloring -- but I've seen variously named versions -- "multiple", "multi-coloring", "advanced coloring", "coloring-recoloring", "supercoloring", etc. The descriptions in the programmer's forum are mostly beyond me. I understand enough that at least *some* of it is not suitable for a human to use, but it's hard to tell which is which.

[Jeff]

Does someone want to take a crack at explaining for *non-programming human solvers* -- to whatever degree they *can* be explained -- the variously named coloring tactics? Maybe with some easy-to-follow diagrams?.

Hi Tso, I would like to take a crack. To my knowledge, there are at least 4 different types of colouring and their names overlap to remind us that our life isn't meant to be easy.

Type 1: colouring that considers bilocation conjugate pairs only, subset of type 2, 3 and 4.
Type 2: colouring that considers all x-cycles (x-wing and turbot fish included), subset of type 3 and 4
Type 3: colouring that considers the combination of x-cycles and xy-chains as discussed here,
Type 4: colouring that considers grouped x-cycles as discussed here.

Simple-colouring has an overlapped meaning for type 1 or anything other than type 3 and 4.
Multi-colouring or Multiple-colouring has an overlapped meaning for type 2 or type 3.
Advanced-colouring means type 3
Super-colouring means type 3
Colouring has an overlapped meaning for type 1, 2, 3 and/or 4.

To avoid the overlapped terms and ambiguity during our discussion, perhaps we should temporary refer:

Type 1 as basic-colouring, as decribed in Angus' Solving Sudoku helper
Type 2 as x-cycle as discussed here, coloring restricted to a single digit, x-wing and turbot fish included)
Type 3 as colouring-table as discussed here
Type 4 as grouped-colouring as discussed here

I understand simple coloring

You only think you understand simple colouring. In fact, simple colouring can be the basic-colouring as decribed in Angus' Solving Sudoku helper or the x-cycle as discussed in Sadman Page.

[Carcul]

Hi Jeff.

Could you (or someone) explain briefly, since I have never used coloring, what is the relation between these various types of coloring and the various types of nice loops?

Thanks in advance.

Regards, Carcul

[Jeff]

what is the relation between these various types of coloring and the various types of nice loops?

Basic-colouring and x-cycle are special cases of simple combination nice loops that involve only one digit.
Colouring-table is equivalent to simple combination nice loops.
Grouped-colouring is equivalent to strong grouped nice loops that involve only one digit.

[angusj]

Unfortunately there's currently no consensus on colour naming.
The only consensus so far is that coloring applies to 'conjugate' candidates (whether they be 'strongly' linked or otherwise). Other than that, it's a bit of a mess and confusing to just about everyone.

While obviously I prefer my own naming conventions, I fully understand that others almost certainly prefer theirs. Having said that, I'm happy to modify my own naming conventions if a majority of interested parties can reach a consensus.

Anyhow, here are a couple of links to my current coloring definitions:
http://angusj.com/sudoku/hints.php#colors
http://www.setbb.com/phpbb/viewtopic.php?p=2575&mforum=sudoku#2575

Notes:
1. I would be very happy to include Turbot fish as a subset of colouring.
2. I would argue against the X-Wing being related to coloring because its more generalised forms (Swordfish, Jellyfish etc) cannot be defined/explained using conjugate relationships.

[Jeff]

While obviously I prefer my own naming conventions, I fully understand that others almost certainly prefer theirs. Having said that, I'm happy to modify my own naming conventions if a majority of interested parties can reach a consensus.

Hi Angus, I would like to pay tribute to your compatibility and flexibility. Let’s gather more opinions from the colouring authors and users, at basic and advanced levels.

BTW, I just want to point out that, correct me if I am wrong, your current names for colouring are:

Type 1: Solving by colours or Simple-colouring as referred by some users.
Type 2: Multi-colouring or Multiple-colouring.

[Jeff]

I would argue against the X-Wing being related to coloring because its more generalised forms (Swordfish, Jellyfish etc) cannot be defined/explained using conjugate relationships.

x-wing is just an x-cycle of non-repetitive type consisting of 2 conjugate links and 2 non-conjugate links. Being non-repetitive, eliminations are outside the loops.

However, I don't mind if you don't want to regard x-wing as colouring. Traditionally, colouring only covers repetitive eliminations.

[angusj]

correct me if I am wrong, your current names for colouring are...

No. Here's my current colour naming conventions:

1. Simple Colours: Colour a single conjugate chain following a single candidate to reveal exclusions as illustrated here. (2 subtypes as illustrated.)
2. Multiple Colours: Colour more than one conjugate chain following a single candidate to reveal exclusions as illustrated here. (2 subtypes as illustrated.)
3. Advanced Colours: Colour more than one conjugate chain following more than one candidate to reveal exclusions. (Pretty much beyond the patience of human solvers.)

Edit: Here are 3 threads from the Programmers' Forum that may provide some background:
http://www.setbb.com/phpbb/viewtopic.php?t=67&mforum=sudoku
http://www.setbb.com/phpbb/viewtopic.php?t=263&mforum=sudoku
http://www.setbb.com/phpbb/viewtopic.php?t=197&mforum=sudoku

[Jeff]

3. Advanced Colours: Colour more than one conjugate chain following more than one candidate to reveal exclusions.

Thanks Angus for the correction. At least everyone agrees advanced-colouring being Type 3.