3-Color rule

[ManSkirtBrew]

Someone pointed me at Dan's Cube Station to help me with my cross solving. I am now thoroughly confused and have some questions.

I'm looking at the second example on the cross solving example page. Scramble: F2 D2 U' R' L2 B2 U L' F U' R' D' B' U2 F'

I get the first paragraph. About halfway through the second, my brain explodes. I've been staring at this text for 15 minutes and it's just not sinking in:

Which way do we need to move the D-layer to get the Orange/White in the correct position to solve the Blue/White? A little trick can help us see quickly. The colours we are considering are Blue and Orange. Since the Blue/White edge is connected to the Orange center, we must match up the Orange/White with the Green center. It is easy to see why, if you matched the Orange/White with the Blue center you would get a pattern where Blue matches with Orange and Orange matches with Blue and this is clearly unresolvable. So when you see a situation like this, always avoid this pattern, and use the 3-colour rule. If you didn't follow this explanation, please read again, it is an important trick to learn.

Easy to see why, huh? Thanks.

What part of the 3-color rule tells me to match orange with green center when blue is matched with the orange center? According to the rule on the first page, it is solvable, since there is red, blue and orange. I got that much. However the rule doesn't say what to do at that point.

Thanks for any help,

-Joe

 

[Chapuunka]

I think it would just be easier to learn your color scheme and not pay attention to center colors (besides white, of course) until your cross is constructed. But that's just me.

 

[dbax0999]

You have blue and orange, if you matched with the blue center there'd be only 2 colors. If you matched with green center that'd be the third color.

 

[ManSkirtBrew]

Ok, I think I see. Since we know it can't be the red, and we already have blue and orange, that only leaves green?

Sorry if this seems obvious. It's just not clicking.

-Joe

 

[frogmanson]

Basically he's saying to solve your cross without aligning to the centers, since the blue/white piece is connected to the orange center, the orange/white should be connected to the green center because on the cube green is on the left of orange, and if you solve the cross without aligning the centers first the cross pieces, orange/white is also on the left of blue/white on the cube. (Do a D move to align centers)

Sorry if this wasn't very eloquent, it was really hard to explain my thought >.<

 

[Anonymous]

It's almost like in the first few seconds of inspection, you don't care about relative position, and you just want to get white pieces down there. As you're debating which route to take to do so, you have to visualize the result of each possible course of action. That's where the three-color rule comes in. That's when you think, "Okay, so doing this little trick will put the orange and blue cross pieces next to each other. I know that they're not opposites, and neither of them will be matched up with its center once I'm done, so I can use the three-color rule."

And that's basically it. The three-color rule itself states that if you're not dealing with either 1) cross pieces matched up to an opposite center, or 2) cross pieces matched up to the correct center, then whenever you look at two adjacent cross pieces AND the centers they happen to be connected to, you'll only see three colors.

Scramble your cube, solve the cross, then do a D'. Look at the blue and red cross pieces. We're just looking at them and the centers. So far, we've counted two colors- blue and red. Blue is connected to the orange center, which makes a third color. However, red is connected to blue, which we've already counted as a color. That means that we're only seeing three colors, and these two cross pieces are correct relative to each other.

One more thing about what I said earlier- It would be horribly inefficient during inspection to plan out an entire cross and ignore relative position. In practice, what happens is that the two kind of meld- you'll be applying the three-color rule and planning your possible options at the same time... if that makes any sense.

 

[ManSkirtBrew]

Ok, now it's starting to sink in. I can't see all the cross moves in advance, but I get how the 3-color rule works. It's definitely cutting way down on the number of moves I'm using for the cross.

Thanks for the help.

-Joe