# Simple Coloring

Part of a family: Chaining-Family

## Description

### General

Simple Coloring is the easiest coloring technique. Coloring is a family of techniques where you color (group) candidates/cells so that they somehow reveal impossible candidates. In case you think this technique requires crayons and you don't feel like using them, don't worry. The coloring is only for clarification and does not require actual coloring with pencils when solving Sudoku puzzles. (More on this later.)

For Simple Coloring we first need to know what strong links and weak links are.

If, in any region, a specific candidate can only be in two cells, then those cells/candidates are considered strongly linked.

In this example, 2 is strongly linked to 2. I.e.

• if 2 is solution, then 2 is not.
• if 2 is not solution, then 2 is.

If, in any region (row, column or box), a specific candidate can be in three or more cells, then those cells/candidates are considered weakly linked.

In this example, 2 is weakly linked to 2. I.e.

• if 2 is solution, then 2 is not.

(Note that with a weak link we cannot know whether 2 is the solution if 2 is not, because there will always be another cell 2 which could also be the solution.)

### Simple Coloring

Here we have a strong link between 6 and 6.

We know that if one of them is the solution, then the other one is not (and vice versa).

Here we have another strong link between one of them and another one. Again, we know that if one of them is the solution, the other one is not (and vice versa).

Furthermore can we say that either all candidates are the solution or all candidates are, because they are alternating.

And here is another strong link directly appended to the chain of strong links.

Since we know that either all candidates are the solution or all candidates are, we know that all cells that see both colors cannot be that candidate.

So 6 can never be the solution, regardless of whether it will turn out to be this...

... or this.

## In short

For Simple Coloring you need to

• find a chain of strong links (only two possible cells for a candidate within the same region)
• color their cells/candidates alternately in two colors (/)
• eliminate all candidates that see both colors ()

## When solving with pen and paper

In case you solve with pen and paper, you don't need to color all cells/candidates.

You can also simply count all the strong links between your chain.

If the chain consists of an odd number of strong links, then its two ends are of different colors, and all candidates who see them can be eliminated. With an even number, it does not work.

In this example, we have three strong links, so we can eliminate.

## Simple Coloring Examples

possible solution group
possible solution group
the candidates we can eliminate

## Sudokus

In this Sudoku we can eliminate eight or nine candidates through Simple Coloring (depending on whether you spot the swordfish).

This Sudoku only needs Simple Coloring and easier techniques.

Go ahead, and try it by pressing the little "Play" button below the grid.