Professors Cube: Difference between revisions

Revision as of 18:48, 21 April 2019

Like the 3x3 and 4x4 cubes, the 5x5 cube can be represented using a tuple, with one entry in the tuple per face of the cube.

The 3x3 cube has 3^2 = 9 faces per side, for a total of 6 x 9 = 54 faces, so the state of any 3x3 cube can be represented using a 54-uple.

The 4x4 cube has 4^2 = 16 faces per side, for a total of 6 x 16 = 96 faces, so the state of any 4x4 cube can be represented using a 96-uple.

The 5x5 cube has 5^2 = 25 faces per side, for a total of 6 x 25 = 150 faces, so we can write the state of any 5x5 cube using a 150-uple.

For general information on the mathematical representation of the cube:

For information specific to the 5x5 cube:

Professors Cube/Numbers - counting the various possible states of a 5x5 cube
Professors Cube/Tuple - representing the various possible states of a 5x5 cube in unique ways
Professors Cube/Permutations - utilizing permutation algebra to manipulate the 5x5 cube

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 ==Algorithms==
+==Mathematical Representation==
+Like the 3x3 and 4x4 cubes, the 5x5 cube can be represented using a tuple, with one entry in the tuple per face of the cube.
+The 3x3 cube has 3^2 = 9 faces per side, for a total of 6 x 9 = 54 faces, so the state of any 3x3 cube can be represented using a 54-uple.
+The 4x4 cube has 4^2 = 16 faces per side, for a total of 6 x 16 = 96 faces, so the state of any 4x4 cube can be represented using a 96-uple.
+The 5x5 cube has 5^2 = 25 faces per side, for a total of 6 x 25 = 150 faces, so we can write the state of any 5x5 cube using a 150-uple.
+For general information on the mathematical representation of the cube:
+* [[Rubiks Cube/Tuple]]
+* [[Rubiks Cube/Permutations]]
+For information specific to the 5x5 cube:
+* [[Professors Cube/Numbers]] - counting the various possible states of a 5x5 cube
+* [[Professors Cube/Tuple]] - representing the various possible states of a 5x5 cube in unique ways
+* [[Professors Cube/Permutations]] - utilizing permutation algebra to manipulate the 5x5 cube
 ==Flags==