The simple cube game is so complex that there are over 43 quintillion (4.3252x1019) states, and any of them can be reached from any other.
While one could spend a lifetime checking each configuration to see if it leads to the solution, there are a whole host of solutions published on the web.
But, what is the fastest way to solve a Rubix cube?
Can a Rubik's Cube be Solved in 20 moves?
A team of researchers found that every possible configuration of the Rubix Cube can be solved in 20-moves or less.The maximum number of moves it takes to solve the Rubik's Cube using the most efficient algorithms possible is called God's Number.
In 1981, it was thought to be as high as 52 (fifty-two). By 2005 it was at 28 (twenty-eight). And now, using a program that can solve the Rubik's Cube in 20-seconds over 35 CPU-years of idle computer time donated by Google, it's been proven to be exactly 20 moves.
Of course, for the true Cube-heads, there's plenty of interesting math behind the discovery. For the rest of us, there's just the nagging knowledge that we've gone about 400-rotations too far.
What is the minimum number of moves to solve a Rubik's Cube?
While the maximum number needed has been adequately and accurately described earlier, the global minimum is zero.The minimum number of moves for any position is not really a number—any given position has its own minimum, and the minimum of these minimums is zero.
There's also debate as to how to measure these moves: if we turn a layer 2-consecutive 90° turns, should that count as 1 or 2-moves?
The least possible number of moves is known as God's number that is 20 moves.
Every position of Rubik's Cube can be solved in 20-moves or less.
With about 35 CPU-years of idle computer time donated by Google, a team of researchers has essentially solved every position of the Rubix Cube, and shown that no position requires more than 20-moves.
We consider any twist of any face to be one move (this is known as the half-turn metric.)
Every solver of the Rubik's Cube uses an algorithm, which is a sequence of steps for solving the Rubik's Cube.
One algorithm might use a sequence of moves to solve the top-face, then another sequence of moves to position the middle-edges, and so on.
There are many different algorithms, varying in complexity and number of moves required, but those that can be memorized by a mortal typically require more than 40-moves.
How many moves does it take to solve a Rubix Cube?
One may suppose God would use a much more efficient algorithm, one that always uses the shortest sequence of moves; this is known as God's Algorithm.The chances of generating a random scramble that can only be solved in 20-moves, no more no less, is around 1 (one) in a billion.
However, the number of combinations that can be solved in 19-moves is approximately 1.5 quintillion. This means that God’s Number is much closer to 19 than 20, but unfortunately even if only 1 (one) scramble sequence was impossible to solve in less than 20-moves.
The number of moves this algorithm would take in the worst case is called God's Number. At long last, God's Number has been shown to be 20.
God’s Number for the 2x2 cube puzzle (having only 3,674,160 different positions) has been proven to be 11-moves using the half turn metric, or 14 using the quarter turn metric (half turns count as 2 rotations).
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