Rubix Cube God's Number Devil's Algorithm Puzzle

https://steemit.com/puzzle/@j1337/solving-the-rubix-cube-s-with-god-s-number-s-and-the-devil-s-algorithm-s-777

The Rubik's Cube is perhaps the world's most famous and iconic puzzle, well-known to have a rich underlying mathematical structure which is group theory. The Rubik's Cube also has a rich underlying algorithmic structure in the : n x n x n Rubik's Cube, as well as the n x n x 1 variant, has a God's Number  this is the diameter of the configuration space of Theta(n^2/log n). The upper bound comes from effectively parallelizing standard Theta(n^2) solution algorithms while the lower bound follows from a counting argument. The upper bound gives an asymptotically optimal algorithm for solving a general Rubik's Cube in the worst case. Given a specific starting state, we show how to find the shortest solution in an n x O(1) x O(1) Rubik's Cube. Finding this optimal solution becomes NP-hard in an n x n x 1 Rubik's Cube when the positions and colors of some of the cubes are ignored.

God’s Number, as many cube enthusiasts will already know equals the maximum number of moves required to solve is exactly 43,252,003,274,489,856,000 combinations of the cube. It has been proven that this number is 20  however the discovery is fairly recent (July 2010). The term God’s Number was coined because the mind of a being able to find the shortest sequence of moves to solve any scramble sequence would have to be thousands of times more powerful than our own, able to test millions of different combinations in the blink of an eye, something that mathematicians believe only a Deity could possess. You can  partitioned the positions into 2,217,093,120 sets of 19,508,428,800 positions each. You also can  reduced the count of sets we needed to solve to 55,882,296 using symmetry and set covering with only solutions of length 20 or less and you can solve a single set in about 20 seconds with some advanced programming using algorithms. It would take you 35 CPU years as it is on a four-core, 2.8GHz equals 1.1 billion seconds and that is to find solutions to all of the positions in each of the 55,882,296 sets.  Visually this is how the numbers would look like within the 20 length.

0	1
1	18
2	243
3	3,240
4	43,239
5	574,908
6	7,618,438
7	100,803,036
8	1,332,343,288
9	17,596,479,795
10	232,248,063,316
11	3,063,288,809,012
12	40,374,425,656,248
13	531,653,418,284,628
14	6,989,320,578,825,358
15	91,365,146,187,124,313
16	about 1,100,000,000,000,000,000
17	about 12,000,000,000,000,000,000
18	about 29,000,000,000,000,000,000
19	about 1,500,000,000,000,000,000
20	about 490,000,000


The number of combinations that can be solved in 19 moves is approximately 1.5 quintillion. This means that God’s Number is much closer to 19 than 20, but unfortunately even if only 1 scramble sequence was impossible to solve in less than 20 moves, God’s Number would still be 20.

In 1980 a lower bound of 18 had been established for God's Number by analyzing the number of effectively distinct move sequences of 17 or fewer moves, and finding that there were fewer such sequences than Cube positions. The first upper bound was probably around 80 or so from the algorithm in one of the early solution booklets.

Below is the hardest position for the programs.
>F U' F2 D' B U R' F' L D' R' U' L U B' D2 R' F U2 D2

So God's Number is equal to 20 for solving the Rubix Cube.

Only 4% needs o be tested of the enormous number of 43 quintillion possible positions that would be exactly 1,802,166,800,000,000,000.


God’s Number for the 2x2 puzzle which has only 3,674,160 different positions has been proven to be 11 moves using the half turn metric, or 14 using the quarter turn metric and that is half turns count as 2 rotations. Unfortunately God’s Number has yet to be calculated for the 4x4 cube, or higher.

There is also a thing called the Devil's Number as well as it uses's the Devil's algorithm and that is looking for the smallest number of moves needed to visit every position at least once. One algorithm that applied repeatedly to any scramble will return to the solved state, not necessarily at the end of of the sequence. SO this Devil's Number is the amount of moves in the shortest algorithm that does this. Imagine that you could solve the Rubik's Cube knowing just one algorithm. The problem is that this would be extremely long. Finding the Devil's algorithm is much much harder than finding the optimal solution. The fact is that we still don't know the Devil's algorithm for the 2x2x2 cube, despite that it has much fewer possible positions. So don't expect this to be found for the Rubik's Cube any time soon. Unfortunately the numbers are so imaginably high that even the 2x2x2 attempts have failed.


God's number became 26 quarter turns, instead of 20 blending quarter turns and half turns when actually a half turn is just two quarter turns in the same direction. The fact that there where millions of positions not meanifully related that were 20 move in the htm suggested the lack of meanifulness of the "God's number is 20 conclusion." In the qtm, only three positions which are 26 moves optimally, all are one isomorph, which is the 4 spotted Super Flip, not the Super Flip which only takes 24 moves.


The total number of states for the Restricted Pocket Cube is only 24.


0	1
1	6
2	27
3	120
4	534
5	2256
6	8969
7	33058
8	114149
9	360508
10	930588
11	1350852
12	782536
13	90280
14	276
Total=3674160
So we can see that there are 3674160 unique configurations of the Pocket Cube, and you need at most 14 moves to solve any one of them.

A1..A3674160.
Inverses = A'1..A'3674160.
D = A1A'1A2A'2..A3674160A'3674160.

AiA'i = i < n

D = N1->2N2->3...N3674159->3674160N3674160->1

The Devil's Number for the Pocket Cube is 102061. It is an equivalent member of the cube permutation group much like another algorithm that performs the same operation of length 14 or less.

1	4
3	90
5	180
7	252
9	324
11	396
13	468
15	540*
17	612*
19	684*
21	756*
23	828*
25	900*
27	972*
29	1044*
31	1116*
33	1188*
35	1260*
37	1332*
39	1404*
41	1476*
43	1548*
45	1620*
47	1692*

The Devil's Number is around 102060 (2 * x + 3), which is extremely close to my prediction of 102061.


To take apart the Rubik's Cube rotate one face 45 degrees and pop out an edge and you will see that it has a core mechanism and the center pieces hold the edges and corners together. You will only have a 1/12 chance of your puzzle being solvable after you put the pieces back together randomly and not in the solved state. Chuck Norris can solve the cube just by staring at it probably our research suggests in 3.3 seconds flat.

 If you line up that many cubes it would reach out 260 light years or it could cover the Earth with 300 layers of cubes as each piece in this huge pile would be showing a unique pattern and only one of them would be solved.

The World Cube Association regulates and holds Rubik’s Cube competitions worldwide since 2004 with officials in 70 countries and the most important event is the Rubik's Cube single but there are one-handed, blindfolded, feet only and fewest moves challenges and it is called Speedcubing.

Feliks Zemdegs is holding the record for the fastest solution on an official competition with an astonishing 4.22 seconds result. Not the first to solve the Rubik's Cube under 5 seconds however.

Speedcubers are quick but a robot called Sub1 solved the cube in 0.887 seconds. It used two webcams to capture the arrangement of the sides, then it calculated the solution and an Arduino-compatible microcontroller board applied the 20 steps. The MultiCuber 999 robot is not so fast but it also achieved a Guiness world record by solving a 9x9x9 cube.

33x33x33 Rubik's Cube is a custom twisty puzzle designers are pushing the limits of big cubes. Currently the largest NxNxN cube is made by Greg's Puzzles and it contains 6153 3D printed parts.


26 cubes consist of the cube designed by Erno Rubik.


The numbers of God are 7 and 3 which both are considered perfect numbers under Hebrew tradition and they even use  1 quite often. [7+3] & 1 = 11.  Christian denominations consider seven to be a holy number because Genesis says that God rested on the 7th day and man was created on the 6th day. The number 777, as triple 7, can be contrasted against triple 6, for the Number of the Beast as 666 rather than variant 616.  ‎ΨΟΖ´; ‎LL36;DCCLXXVII;1100001001;2

The number 7 signifies completion or perfection, as seen in Genesis 7:2 - 4, Revelation 1:20. It is called God's number. No surprise even 1 is obviously used throughout the Bible to indicate one thing only, God Himself. “The one true God.” The number 1.   Psalms 18:31. All God's ways are perfect.


“Hear, O Israel: The Lord our God, the Lord is one” (Deuteronomy 6:4). God is the only God. “You shall have no other ... The number “13” is a number of great blessings given by God.


1337 Skillz all day
J-Qubed