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God's Algorithm

2017-12-18T20:09:38Z

Ajayijoshua8: /* God's Number */

'''God's Algorithm''' is the optimal [[solve|solution]] from a puzzle state to another [[cube state|state]], commonly the [[solved cube state|solved state]]. The term is sometimes used to refer to the [[algorithm]] itself, or an algorithmic procedure that finds such a solution efficiently.

== God's Number ==
'''God's Number''' is either used to refer to the diameter of the [[Rubik's Cube Group|group]] of the puzzle (the furthest distance two states can be from each other) or to the furthest distance any position can be from solved. God's Number has long been known for smaller puzzles, such as [[2x2x2]] and [[Pyraminx]], but for [[3x3x3]] it was unknown until July 2010 and it is still unknown for bigger cubes (like the [[4x4x4]]).

=== [[3x3x3]] ===
* In July 2010, [[Morley Davidson]], [[John Dethridge]], [[Herbert Kociemba]], and [[Tomas Rokicki]] proved God's Number for [[3x3x3]] to equal 20 in [[HTM]]. The [[superflip]] is the best-known example of a position which requires 20 moves or more to solve in [[HTM]].
* In August 2014, [[Morley Davidson]], [[John Dethridge]], and [[Tomas Rokicki]] proved God's Number for [[3x3x3]] to equal 26 in [[QTM]]. The [[superflip plus fourspot]] is the first proved example of a position which requires 26 moves or more to solve in [[QTM]].
* The God's number in [[slice turn metric]] (STM) is still unknown; there is a lower bound of 18s and an upper bound of 20s. [http://cubezzz.dyndns.org/drupal/?q=node/view/200]

=== [[4x4x4]] ===
* In the outer block turn metric (OBTM), the God's number for 4x4x4 is known to be between [http://cubezzz.dyndns.org/drupal/?q=node/view/236 35] and [http://cubezzz.dyndns.org/drupal/?q=node/view/541 55] moves.
* In the single-slice turn metric (SSTM), the God's number is known to be between [http://cubezzz.dyndns.org/drupal/?q=node/view/236 32] and [http://cubezzz.dyndns.org/drupal/?q=node/view/541 53] moves.
* In the block turn metric (BTM), the God's number is known to be between [http://cubezzz.dyndns.org/drupal/?q=node/view/236 29] and [http://cubezzz.dyndns.org/drupal/?q=node/view/541 53] moves.

=== [[5x5x5]] ===
* In OBTM, the God's number for 5x5x5 is known to be between [http://cubezzz.dyndns.org/drupal/?q=node/view/236 52] and [//www.speedsolving.com/forum/threads/5x5x5-obtm-upper-bound.61270/ 141] moves.

=== [[Megaminx]] ===
* The God's number for the Megaminx is known to be between 48 and 194 [[FTM|face turns]]. [//www.speedsolving.com/forum/threads/approximating-dodecahedron-upper-bound.65036/]

== External links ==
* [http://cube20.org God's number in HTM is 20]
* [http://cube20.org/qtm God's number in QTM is 26]
* [https://en.wikipedia.org/wiki/God%27s_algorithm God's algorithm] in Wikipedia

[[Category:Puzzle theory]]

God's Algorithm

2017-12-18T20:08:42Z

Ajayijoshua8: /* God's Number */

'''God's Algorithm''' is the optimal [[solve|solution]] from a puzzle state to another [[cube state|state]], commonly the [[solved cube state|solved state]]. The term is sometimes used to refer to the [[algorithm]] itself, or an algorithmic procedure that finds such a solution efficiently.

== God's Number ==
'''God's Number''' is either used to refer to the diameter of the [[Rubik's Cube Group|group]] of the puzzle (the furthest distance two states can be from each other) or to the furthest distance any position can be from solved. God's Number has long been known for smaller puzzles, such as [[2x2x2]] and [[Pyraminx]], but for [[3x3x3]] it was unknown until July 2010 and it is still unknown for bigger cubes (like the [[4x4x4]]).

=== [[3x3x3]] ===
* In July 2010, [[Morley Davidson]], [[John Dethridge]], [[Herbert Kociemba]], and [[Tomas Rokicki]] proved God's Number for [[3x3x3]] to equal 20 in [[HTM]]. The [[superflip]] is the best-known example of a position which requires 20 moves or moves to solve in [[HTM]].
* In August 2014, [[Morley Davidson]], [[John Dethridge]], and [[Tomas Rokicki]] proved God's Number for [[3x3x3]] to equal 26 in [[QTM]]. The [[superflip plus fourspot]] is the first proved example of a position which requires 26 moves or more to solve in [[QTM]].
* The God's number in [[slice turn metric]] (STM) is still unknown; there is a lower bound of 18s and an upper bound of 20s. [http://cubezzz.dyndns.org/drupal/?q=node/view/200]

=== [[4x4x4]] ===
* In the outer block turn metric (OBTM), the God's number for 4x4x4 is known to be between [http://cubezzz.dyndns.org/drupal/?q=node/view/236 35] and [http://cubezzz.dyndns.org/drupal/?q=node/view/541 55] moves.
* In the single-slice turn metric (SSTM), the God's number is known to be between [http://cubezzz.dyndns.org/drupal/?q=node/view/236 32] and [http://cubezzz.dyndns.org/drupal/?q=node/view/541 53] moves.
* In the block turn metric (BTM), the God's number is known to be between [http://cubezzz.dyndns.org/drupal/?q=node/view/236 29] and [http://cubezzz.dyndns.org/drupal/?q=node/view/541 53] moves.

=== [[5x5x5]] ===
* In OBTM, the God's number for 5x5x5 is known to be between [http://cubezzz.dyndns.org/drupal/?q=node/view/236 52] and [//www.speedsolving.com/forum/threads/5x5x5-obtm-upper-bound.61270/ 141] moves.

=== [[Megaminx]] ===
* The God's number for the Megaminx is known to be between 48 and 194 [[FTM|face turns]]. [//www.speedsolving.com/forum/threads/approximating-dodecahedron-upper-bound.65036/]

== External links ==
* [http://cube20.org God's number in HTM is 20]
* [http://cube20.org/qtm God's number in QTM is 26]
* [https://en.wikipedia.org/wiki/God%27s_algorithm God's algorithm] in Wikipedia

[[Category:Puzzle theory]]

Big cube

2017-12-18T19:32:17Z

Ajayijoshua8: /* The largest cube */

[[Image:Wiki 7x7x7 solved.jpg|160px|thumb|An example of a (very) big cube.]]
'''Big Cubes''' (also known as ''bigcubes'' or ''NxNxN cubes (N>3)'') are [[cube|cubical]] [[puzzle]]s having an order larger than the usual [[3x3x3 cube]]. Until the release of [[V-cube]]s, the only mass-produced big cubes were the [[4x4x4 Cube]] and the [[5x5x5 Cube]]. With the V-cube technology it is now possible to mass-produce larger cubes, even up to the [[11x11x11 Cube]]; already, it is possible for anyone to buy the [[6x6x6 Cube]] and the [[7x7x7 Cube]]. A cube of any size can exist in theory, but the largest cubes can only be played with on computer simulators such as [[Gabbasoft]] or [[IsoCubeSim]]. In computer simulators, virtually any size is possible (although the larger the size is the slower the program will run), but very few people have ever attempted any cube larger than the [[20x20x20 Cube]].

There are many methods for solving big cubes in general:
* The [[Reduction method]], by far the most common big cubes method, takes advantage of the fact that big cubes are composed of [[corner]]s (three [[sticker]]s per piece), groups of [[edge]]s (two stickers per piece), and groups of [[center]]s (one sticker per piece), arranged in the same way as in the [[3x3x3 cube]]. The solver groups all the centers by color using intuitive [[block building]] techniques, then groups all of the edges by color using [[commutator]]-like moves, and finally solves the rest of the cube by turning only the outer layers and treating it like a [[3x3x3 cube]].
* The [[K4]] method, invented by [[Thom Barlow]], is designed for the [[4x4x4 Cube]] but has been extended to larger cubes. The solver first builds two opposite groups of centers and uses blockbuilding to create a 1x(N-1)xN block (where N is the size of the cube). Then, the solver puts that block on L and finishes the remaining center groups without breaking the block. The next step is to pair up a fourth edge group and finish the L layer, and then place that layer on D. Finally, the solver uses CLL to solve the corners and finishes all of the edge pieces with [[commutator]]s.
* The [[Cage]] method is a method that solves all of the center pieces last, and has the advantage of being able to deal with parity very easily. The first step is to solve all of the edges and corners (relative to the fixed centers if there are any), which can be done many different ways and varies depending on the cuber. After that, the centers are all solved with [[commutators]], typically one or two at a time.
* Less popular (and often unnamed) methods include layer-by-layer solving; using columns to build the first N-1 layers; creating and expanding a block of pieces until only two adjacent layers are left; solving the centers and corners first; and solving the first and last layers, then the middle layer edges, and finally the rest of the centers.

== The largest cube ==
As of 18 December 2017, the largest order cube is a [https://www.youtube.com/watch?v=NqJC3YxfcyM 33x33 cube] made by YouTube user Greg's Puzzles.

Prior to this, the largest order magic cube was 17x17x17 cubes large and consists of 1,539 parts. It's called "Over The Top" and was created by Oskar van Deventer (Netherlands) and was presented at the New York Puzzle Party Symposium in New York, USA, on 12 February 2011. Record was accepted by Guinness World Records. It is the largest cube available to the public, if at a high price. On 4 March 2017, [[YuXin]] announced a commercially available 17x17 cube via Facebook.
[[File:17x17x17.jpg|none|thumb|17x17x17]]

== See also ==
* [[Big Cube methods]]
* [[4x4x4 methods]]
* [[5x5x5 methods]]

[[Category:Twisty puzzles]]