God's Algorithm

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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]

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