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 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).
- 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 moves to solve in QTM.
- 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.