1Definition: Simple Coloring is a chaining technique which reveals a "Single's Chain," where the links in the chain are all between a single digit's Conjugate Pairs (so they are all "strong" links). The coloring comes into play when we highlight each digit in alternating colors. Then, any cell outside the chain that can see both colors can have its matching digit erased.
Simple Coloring on digit 7 Conjugate Pairs: 7's outside the chain that see 7's of both colors can be erased (yellow cells)
2Look For: Conjugate Pairs (CPs). At least two of them, but the more the better. Take a look at this example.In Sue, the Tool tab will show you the number of CPs each digit has, and you can use the number buttons to highlight the CPs, as we have done in this example, to highlight Conjugate Pairs for digit 7.
We can see that there are plenty of CPs for digit 7, and lots of candidate 7's outside the chain that are likely to see two different colors. So, our next step would be to highlight the 7s in the chain with alternating colors (using Sue's Draw Mode/Simple Coloring from the Tool tab), then look for 7s outside the chain that can see two differently colored 7s.
3Consequence: Any cell outside the chain that can see two differently colored candidates can have its matching candidate erased.In our example, that would be the 7s at:
C4, which can see the blue 7 at D4 and the orange 7 at B6.
G9, which can see the blue 7 at G6 and the orange 7 at C9.
H9, which can see the blue 7 at H2 and the orange 7 at C9.
4Why it Works: In a CP, we know that one end will be true and the other will be false. If two or more same-digit CPs are linked together (i.e. share a common cell) then we can extend that logic all along the chain, with all even nodes sharing one logical state (true or false), and all odd nodes sharing the opposite state. Coloring makes it easy to visualize the odd (e.g. blue) vs. the even (e.g. orange) nodes.
5So, in the end we can confidently say: "All nodes of the same color share the same logical state" (e.g. "Either all blue digits are true and orange digits are false, or vice-versa"). When a cell outside of the chain can see both colors (i.e. it sees both a true and a false node) we know that the seeing cell cannot contain the digit in question, because it sees a cell that is true for that digit (even though we don't know which one it is; we know it is one of them, and that's enough to rule out the seeing cell from ever being that digit).
6Type 2: Take a look at this Type 2 example.Clicking on the 1 button in the Tool tab, we see lots of CPs.If, after coloring, you find two digits of the same color in a house (such as the two blue 1's in row 1 [and also in column I -- but we only need one instance]), that reveals a contradiction; both cannot be true, therefore all digits of that color are false and can be erased. More importantly, it means that all digits of the opposite color are true! So, you can just go ahead and convert them all to Big Numbers (the opposite colored candidates will automatically erase in Sue). In our example, all orange 1's have been entered as Big Numbers, and all blue 1's have been erased (leaving some naked singles, and a quickly solved puzzle).
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