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Multi-Coloring |
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Multi-Coloring involves two separate Coloring webs of a single candidate value that can be associated. There are two different type of Multi-Coloring:
Type 1:
In Type 1 Multi-Coloring, each color in each web has its counterpart in the other web. This means that at least one candidate in a web shares a unit with a candidate in the other web. Then, any candidate in the puzzle that shares a unit with both of the other colors can be eliminated.
Consider the above example. Two unconnected webs of 9's have been colored, one using yellow-orange, the other green-blue. Notice that two green values from the green-blue web share a unit with an orange value from the yellow-orange web (the same effect would occur if only one green matched up with an orange). Because of this, these webs are associated. If the greens were false, the blues would be true (this is the nature of simple Coloring). If the oranges were false, the yellows would be true. If both are false, then both blues and yellow would be true. Any way it goes, either yellow, blue, or both is true. All of these lead to the elimination of the small 9 highlighted in light-blue (It shares a unit with the opposite colors, yellow and blue.
Type 1 Multi-Coloring can also occur if both colors share a unit with opposite colors. In the example above, if a blue shared a unit with a yellow, then any candidate in the puzzle that shared a unit with both orange and green could also be eliminated.
Type 2:
Type 2 Multi-Coloring is similar to Type 1 Multi-Coloring, except that a color from one web shares a unit with both colors from the other web. This seems to create a contradiction, but in fact it does not. In fact, it simply shows that the second color from the one web is true, and the first color is false.
Consider the above example. Two unconnected webs of 3's are colored, one using yellow-orange, the other green-blue. One yellow from the yellow-orange web shares a unit with a green, and the other with a blue. Since these are mis-matched, this is Type 2 Multi-Coloring. No matter which of the green-blue web is true, one of the yellows has to be false (notice since the webs are not connected, green or blue being false doesn't necessarily make a yellow true). Since by definition of coloring either all yellows have to be true or all yellows have to be false, we now know that since one must be false, they all must be false. By deduction then, the orange cells contain 3's.
Sudoku Snake gives both types of Multi-Coloring a skill value of 750.
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