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 is unknown for 3x3x3, but it is known for many smaller puzzles, such as 2x2x2 and Pyraminx. The superflip is known to require 20 moves in HTM, and Rokicki has proven an upper bound of 22 moves for any position.