Overview[]
God's Number refers to the maximum number of moves required to solve a puzzle from any scrambled position, assuming perfect efficiency. This number has been calculated for several types of Rubik's Cubes through advanced computational analysis. Below are the God's Numbers for different cubes that have been studied.
2x2x2 Cube[]
- God's Number: 11 moves
- Details:
- The 2x2x2, also called the "Pocket Cube," is the simplest version of the Rubik's Cube. Despite its simplicity, calculating God's Number required computational power due to the 3,674,160 possible positions.
- Move Count Metric: Half-turn metric (HTM), where each 90° or 180° turn counts as one move.
3x3x3 Cube[]
- God's Number: 20 moves
- Details:
- This number was confirmed in 2010 by a team of researchers, including Tomas Rokicki and Google's computational resources.
- The 3x3x3 has 43 quintillion possible positions (43,252,003,274,489,856,000), but no position requires more than 20 moves to solve.
- Move Count Metric: Half-turn metric (HTM).
4x4x4 Cube[]
- God's Number: 26 moves (estimated)
- Details:
- The 4x4x4, known as "Rubik's Revenge," introduces center pieces and edge pairing, increasing complexity significantly.
- God's Number for the 4x4x4 is not definitively proven but is estimated to be 26 in the quarter-turn metric (QTM).
5x5x5 Cube[]
- God's Number: Unknown
- Details:
- The 5x5x5, or "Professor's Cube," adds even more layers and complexity.
- Exact God's Number calculations for the 5x5x5 remain unproven due to the exponential increase in possible states.
Pyraminx[]
- God's Number: 11 moves
- Details:
- The Pyraminx, a tetrahedral puzzle, has far fewer positions than a 3x3x3 cube due to its simpler design.
- Calculating God's Number for the Pyraminx is straightforward due to its lower state complexity.
Megaminx[]
- God's Number: Estimated at 77 moves
- Details:
- The dodecahedral Megaminx has significantly more pieces than a standard 3x3x3, leading to a much higher estimated God's Number.
- This estimation uses computational models and assumes optimal solving techniques.
Square-1[]
- God's Number: 13 moves
- Details:
- The Square-1 shape-shifting puzzle requires algorithms that consider its unique geometry.
- Despite its complexity, God's Number remains relatively low compared to higher-layered cubes.
Future Calculations[]
As computational power increases, God's Numbers for more complex cubes (6x6x6 and beyond) may eventually be calculated. These calculations require enormous resources due to the rapidly growing number of possible positions as layers increase.