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2020-06-04T02:51:30Z

Created page with "'''Simple Colors''' is a subtype of coloring which only uses 2 colors. == How it works (1) == The following example demonstrates the principle: Image:Color-trap.png..."

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'''Simple Colors''' is a subtype of [[coloring]] which only uses 2 colors.

== How it works (1) ==
The following example demonstrates the principle:

[[Image:Color-trap.png]]

All the [[candidate]]s for [[digit]] '''3''' are highlighted. When a [[row]], [[column]] or [[box]] contains only 2 candidates for a digit, one of them must be true and the other must be false. These candidates have a [[strong link]]. In coloring terminology, these candidates form a [[conjugate pair]]. We can use colors to help us remember which candidates must be true or false simultaneously. In the example, green and blue colors have been applied. Notice that row 9, column 9 and box 9 all have 2 candidates for digit '''3''', which now have opposite colors.

Now either ''all'' blue cells must contain digit '''3''' or ''all'' green cells. There is no middle ground in which some blue cells and some green cells contain digit '''3'''.

Cell '''r2c6''' can [[see]] both colors. It cannot sustain a candidate for digit '''3'''.
== How it works (2) ==
Here is an example that shows how colors can cause a contradiction.

[[Image:Color-wrap.png]]

All the [[candidate]]s for [[digit]] '''1''' are highlighted.

Now either ''all'' blue cells must contain digit '''1''' or ''all'' green cells.

It is easy to see that it would be impossible for all blue cells to contain digit '''1'''. There are 2 blue cells in row 1, box 2 and column 5. Because ''some'' blue cells are invalid, we can declare ''all'' blue cells unsuitable for digit '''1'''.

This is the basic principle of coloring.

== See also ==
* [[Multi-Colors]]
* [[X-Colors]]

[[Category:Solving Techniques]]

Simple Colors - Revision history

Rooted: Created page with "'''Simple Colors''' is a subtype of coloring which only uses 2 colors. == How it works (1) == The following example demonstrates the principle: Image:Color-trap.png..."