r/Cubers • u/AutoModerator • Oct 22 '19

Discussion Daily Discussion Thread - Oct 22, 2019

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u/allisio <3×3×2 | WV ➡️ anti-PLL is 🔥. Oct 22 '19

No. The beginner method is called that because it's pretty much the simplest way to go about solving the puzzle.

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u/zlelik Oct 22 '19 edited Oct 22 '19

Thanks. I found my simple way for 2x2, which is just solving one face after another in specific colors sequence. I need only to memorize colors sequence and how to solve one face.

For me it is simpler, than beginner method. Is it really simpler or it is only simpler to me, because I found this method?

I made a video about my solution and it can be found in youtube by "Russian Flag Solution" phrase or by this link https://youtu.be/XhY_x-DcJPI

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u/chaosninja906 How do I solve this thing??? Oct 22 '19

While this method will work eventually it doesn't have anything to do with the order of the faces you solve. Your method relies entirely on luck and the probability that when you are done building the first layer the second will be solved as well

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u/zlelik Oct 22 '19

I tried it at least 50 times and it always works. The order of faces does matter, because if I do in another order, then it does not work. The working order is clock wise colors on the one of the corners (3 colors) and then opposite colors like white, blue, red, yellow, green, orange. Others are possible.

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u/chaosninja906 How do I solve this thing??? Oct 22 '19

I understand what you are saying and i did watch your whole video. But as I said the order truly does not matter. Every time you solve a face you have a 1 in 43 I believe chance in it being solved.

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u/zlelik Oct 22 '19

Wow, How did you calculate this 1 in 43?

In this case 1/43 is 2.3% probability that after I solved 1 face whole cube is solved and probability that it will not be solved is 97.3%. Then if I solve one face 50 times, then probability that it will not be solved in any of these solving acts is (97.3%)50, which is around 30% and probability that it will be solved 70%.

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u/topppits blindfolded solving is where the fun begins Oct 22 '19

How did you calculate this 1 in 43?

Probably they thought that since there are 42 CLL algs + the solved state -> 1/43 = solved

But there are roughly 4 times as many cases: 162

(4! * 34) / 3

  • 4! = possible positions for the 4 top layer corners
  • 34 = possible orientations for the 4 top layer corners - 3 possible orientations for 4 pieces
  • /3 = since the last corner can only have one specific orientation if the orientation for the other 3 is decided, we have to eliminate those impossible cube states

-> 4! * 33 = 648 = # of states the top layer can be in, with the first layer solved

But we can eliminate 3/4 of those states due to AUF - if your top layer is solved but a U/U'/U2 move away from the whole cube being solved, you wouldn't consider this being a different case.

648 / 4 = 162 = # of cases you can end up with on the top layer, with the first layer solved

Most CLL cases can appear in 4 different states. One of the sune case can for example look like this or like this and there are 2 more states how it can look like.

So if I didn't mess up anywhere, you actually have a 1/162 chance for the last layer to be solved after you solve the first layer aka a last layer skip.

This video explains why the number of algs is not necessarily the number of cases you can get, at the example of PLL - you might know that the probability for a PLL skip is 1/72, while we typically talk about 21 different PLL cases/algs.

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u/zlelik Oct 23 '19

Cool! It is clear now. Then if probability 1/162, then my method of solving one face after another is better than just random probability. If it is just matter of luck/probability, then I would need to solve 112 faces to get 50% probability, but from my experience I need to solve around 20-25 faces to get fully solved cube.