Zane's TuRBo Edge Tutorial

I think I made it more confusing by trying to simplify part 4. Is there anything you specifically you find confusing, or just part 4 in general?

The even swaps and how you end with a 2-cycle rather than a 3 cycle. You tried explaining it to me once and I still couldn't get it. I don't blame you its just a little over my head.
 
The even swaps and how you end with a 2-cycle rather than a 3 cycle. You tried explaining it to me once and I still couldn't get it. I don't blame you its just a little over my head.
It's not over your head, it just needs to be explained to you in the right way. :)
I'll try again, explaining in a slightly different way from how I first tried.

---------------------------------------------------------------------------
*I'm going to stop using the term '2-cycle', and replace it with parity alg. I probably should've done this in the first place.
*1 swap = swapping 2 pieces with each other.

-A 3-cycle has 2 swaps (ie. for UF>UR>UL, the swaps are: UF-UR and UL-UF)
-A parity alg (such as y-perm) also has 2 swaps (but instead of swapping one type of piece, there is 1 swap of corners and 1 swap of edges).

The total number of swaps needed to solve a cube will ALWAYS be even, this means a 3BLD solve can be deduced to 2 situations:
#1: odd edges and odd corner swaps. (parity)
#2: even edges and even corner swaps.

Imagine yourself in situation #2. Since 3-cycles are even (2 swaps), you can solve the cube with nothing but 3-cycles.

Now imagine yourself in situation #1. No matter how many 3-cycles you do, you won't be able to solve it, because 2 swaps won't ever add to give an odd number of swaps. Therefore you must apply a parity alg to perform 1 edge swap and 1 corner swap.

This provides a detailed explanation of why there will always be an even number of swaps.
 
It's not over your head, it just needs to be explained to you in the right way. :)
I'll try again, explaining in a slightly different way from how I first tried.

---------------------------------------------------------------------------
*I'm going to stop using the term '2-cycle', and replace it with parity alg. I probably should've done this in the first place.
*1 swap = swapping 2 pieces with each other.

-A 3-cycle has 2 swaps (ie. for UF>UR>UL, the swaps are: UF-UR and UL-UF)
-A parity alg (such as y-perm) also has 2 swaps (but instead of swapping one type of piece, there is 1 swap of corners and 1 swap of edges).

The total number of swaps needed to solve a cube will ALWAYS be even, this means a 3BLD solve can be deduced to 2 situations:
#1: odd edges and odd corner swaps. (parity)
#2: even edges and even corner swaps.

Imagine yourself in situation #2. Since 3-cycles are even (2 swaps), you can solve the cube with nothing but 3-cycles.

Now imagine yourself in situation #1. No matter how many 3-cycles you do, you won't be able to solve it, because 2 swaps won't ever add to give an odd number of swaps. Therefore you must apply a parity alg to perform 1 edge swap and 1 corner swap.

This provides a detailed explanation of why there will always be an even number of swaps.

Oh I get it now. Thanks Zane, your awesome :)
 
I may just not be getting this but how do I memo for turbo do I memorize the locations like dl > dr > uf or do I memorize it with a letter scheme? I know all the algs and been trying to figure this out for 2 weeks now.
 
Back
Top