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, when Davidson, Dethridge, Kociemba, and Rokicki proved it to equal 20. The superflip is the best-known example of a position which requires 20 moves to solve in HTM.