Difference between revisions of "God's Algorithm"

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<seo title="God's Number - Optimal Solution to Solve a Rubik's Cube" />
 
'''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 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 ==
'''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 an it is still unknown for bigger cube (as the [[4x4x4]])
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'''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]]).
  
=== God's Number for [[3x3x3]] ===
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=== [[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]].
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* 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 moves to solve in [[QTM]].
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* 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]].
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* 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]
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=== [[4x4x4]] ===
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* 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.
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* 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.
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* 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.
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=== [[5x5x5]] ===
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* 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.
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=== [[Megaminx]] ===
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* 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 ==
 
== External links ==
 
* [http://cube20.org God's number in HTM is 20]
 
* [http://cube20.org God's number in HTM is 20]
 
* [http://cube20.org/qtm God's number in QTM is 26]
 
* [http://cube20.org/qtm God's number in QTM is 26]
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* [https://en.wikipedia.org/wiki/God%27s_algorithm God's algorithm] in Wikipedia
  
 
[[Category:Puzzle theory]]
 
[[Category:Puzzle theory]]

Latest revision as of 07:53, 11 December 2018

God's Algorithm is the optimal solution from a puzzle state to another state, commonly the 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 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

4x4x4

  • In the outer block turn metric (OBTM), the God's number for 4x4x4 is known to be between 35 and 55 moves.
  • In the single-slice turn metric (SSTM), the God's number is known to be between 32 and 53 moves.
  • In the block turn metric (BTM), the God's number is known to be between 29 and 53 moves.

5x5x5

  • In OBTM, the God's number for 5x5x5 is known to be between 52 and 141 moves.

Megaminx

  • The God's number for the Megaminx is known to be between 48 and 194 face turns. [2]

External links