How to solve the 2x2x2 cube completely intuitively?

[bcube]

While reading some old threads, I came across to this request by Thom Barlow. It had been addressed by Michael James Straughan here, as well as by Conrad Rider here.

The Heise method is often suggested when asking for an intuitive 3x3x3 method with 0 algorithms and zero memorization. My first instinct was applying this method to the 2x2x2 cube. But there is a catch: as Ryan Heise pointed out here, In the Heise method, parity is dealt with while solving the last 5 edges. If all edges are solved (which is an even edge permutation), this forces the remaining corners to have even parity. It means you can get a 2x2x2 state which you cannot get with the Heise method on a 3x3x3 cube.

Without further ado, let´s solve the 2x2x2 cube intuitively. This guide is meant to be for beginners, consider it like a beginner version of the Heise method for a 2x2x2 cube if you want.

Step 1: solve a layer
No descriptioon here, you should be able to do that on your own.

Step 2: orient the last layer
If you are lucky, the last layer is already oriented. Otherwise there are 2 groups of cases, both of which can be solved using commutators: either orient some corners both clockwise and counter-clockiwe, or orient 3 corners clockwise (or counter-clockwise). An interactive example solve can be seen below, use the buttons at the top-right to switch between those 2 groups. How to orient a different case should be obvious from the example solves.



1-6: orienting the first corner
7-13: orienting the second corner
14-20: orienting the third corner

Step 3: permute the last layer
Adjust the last layer so that there are 2 solved corners in it (4 solved corners if you are lucky). Both the adjacent corner swap and the diagonal corner swap can not be directly solved by the Heise method and commutators - that is because the corner permutation is odd. You can toggle it to being even by a single quarter turn.



1: toggling the corner permutation from being odd (1 swap of corners needed) to even (2 swaps of corners needed), also solving the corner at URB which will be used as a reference point to the other corners in the last layer
2-9: solving the corner at ULF
10-18: the moves should be obvious



1: toggling the corner permutation from being odd (1 swap of corners needed) to even (2 swaps of corners needed)
2-9: solving the corner at URB
10-17: solving the corner at URF
18-25: the moves should be obvious

And there you have it, you can solve the 2x2x2 cube completely intuitively, using zero memorization.

Feel free to ask if something is not clear to you. Feel free to post another completely intuitive method for solving the 2x2x2 cube.

 

[bldcuber314]

Well one way could be learning how to do commutators, and using those to solve the cube. Of course you could just keep solving one layer intuitively until you get an LL skip, but I guess that doesn't count as a method.

 

[bcube]

Well one way could be learning how to do commutators, and using those to solve the cube.

There is a catch I was talking about earlier. You can´t use just commutators to solve all 2x2x2 states. In fact, you can solve only half of its states using only commutators. Neither of those 2 states in step 3 can be solved using only commutators.

 

[Deleted member 36445]

or you can just use petrus

 

[TyRoJo]

eg1 anyone...

 

[Athefre]

Another way is CPLine > iterative CO > Solve. Or some other finish after CPLine. It's not beginner friendly at all, but is a way to completely understand a solve.

athefre - Iterative Corner Solving

This is a system for intuitively solving the last six corners when the DL corners have been solved and the remaining corners permuted into the RU solvable orbit. I originally had this idea around 2010-2012. The original idea was to solve the 2x2x2 puzzle like Roux LSE using <x, U> instead of <M,

sites.google.com

 

[Caleb Valenzuela]

keep solving one layer and pray that you get a last layer skip

 

[qwr]

keep solving one layer and pray that you get a last layer skip

yeah if you do first layer there's only 7 OLLs and 2 PLLs

 

[efattah]

Sorry to be critical but your method is not intuitive at all, where do the commutator algorithms even come from? If this was obvious then everyone in the 1980's would have done it.
The only way to solve a 2x2 intuitively without any algorithms that I know is the same method we all used in the 1980's, which is to solve the top four corners intuitively, then, for the bottom layer, what you do, is you break off one of the top corners and put it back in a different way. Each time there is a 1 in 42 chance that the bottom corners will be solved, so it takes around 10-30 minutes based on how fast the person turns.
This is the method we used to solve the corners on the 3x3 in the 1980's and the same method Waterman said he used at the very beginning, it was only later that we all developed algorithms to solve the 'bottom' corners and Minh Thai was the first (with the help of his university professor) to generate all 42 algorithms.

NOTE: Even though there is a 1 in 42 chance that the corners are solved, it doesn't happen in 42 tries. Based on probability it often takes 100 or more tries, and some people after 30 tries would just destroy the entire upper face and re-scramble, that is another method, to keep rescrambling and solving the upper layer until you get a CLL skip on the bottom layer.

In the the 1st & 2nd grade people found out I was the only person at school who could solve the cube (in 1981/82) and bullies would surround me and make me solve it or beat me up, it was extremely stressful because it would take 100 tries to get the bottom corners to get solved and they would be staring at me waiting to beat me up. Driven by this fear & stress (on a daily basis), I finally generated 5 algorithms that I could use to orient & permute the bottom corners and after that I could consistently solve the cube in 40-50 seconds.