The Professor's Cube (also known as Rubik's Professor) is a mechanical puzzle invented by Udo Krell. It is a 5×5×5 version of the Rubik's Cube. It has qualities in common with both the original 3×3×3 Rubik's Cube and the 4×4×4 Rubik's Revenge, and knowing the solution to either can help when working on the 5×5×5 cube. Image File history File links This is my Professors Cube. ... A puzzle is a problem or enigma that challenges ingenuity. ... Variations of Rubiks Cubes (from left to right: Rubiks Revenge, Rubiks Cube, Professors Cube, & Pocket Cube) Rubiks Cube (commonly misspelled rubix, rubicks or rubics cube) is a mechanical puzzle invented in 1974[1] by the Hungarian sculptor and professor of architecture ErnÅ‘ Rubik. ... Variations of Rubiks Cubes (from left to right: Rubiks Revenge, Rubiks Cube, Professors Cube, & Pocket Cube) Rubiks Cube (commonly misspelled rubix, rubicks or rubics cube) is a mechanical puzzle invented in 1974[1] by the Hungarian sculptor and professor of architecture ErnÅ‘ Rubik. ... Rubiks Revenge in solved state The Rubiks Revenge is the 4×4×4 version of Rubiks Cube. ...

Workings

Permutations

There are 8 corner cubelets, 36 edge cubelets (two types), and 54 center cubelets (48 movable of two types, 6 fixed).

Any permutation of the corner cubelets is possible, including odd permutations, giving 8! (40 320) possible arrangements. Seven of the corner cubelets can be independently rotated, and the eighth cubelet's orientation depends on the other seven, giving 3⁷ combinations. Permutation is the rearrangement of objects or symbols into distinguishable sequences. ...

Assuming the 4 center cubelets of each type of each colour are indistinguishable, there are (24!/(4!⁶))² or 24!²/4!¹² arrangements, all of which are possible, independently of the corner cubelets.

Identically coloured pairs among the 24 outer edge cubelets cannot be flipped. The two cubelets in each matching pair are distinguishable, since the colours on a cubelet are reversed relative to the other. Any permutation of the outer edge cubelets is possible, including odd permutations, giving 24! arrangements, independently of the corner cubelets and indistinguishable center cubelets. The 12 central edge cubelets can be flipped. Eleven can be flipped and arranged independently, giving 12!/2 × 2¹¹ or 12! × 2¹⁰ possibilities (an odd permutation of the corner cubelets implies an odd permutation of the central edge cubelets, and vice versa, thus the division by 2). Counting the outer edge cubelets, there are 24! × 12! × 2¹⁰ possibilities.

The corner, central edge and fixed center cubelets together form a 3×3×3 Rubik's Cube. In the case that centers of the same color are indistinguishable from each other the remaining cubelets can be arranged independently of it.

This gives a total number of permutations of

The full number is 282,870,942,277,741,856,536,180,333,107,150,328,293,127,731,985,672,134,721,536,000,000,000,000,000 possible permutations, more or less.

Durability

The Professor's Cube is inherently more delicate than the 3×3×3 Rubik's Cube due to the considerable additional movable parts. It is not recommended that it be used for speedcubing. The puzzle should not be excessively forced to twist and it must be aligned properly before twisting to prevent damage. It is far more likely to break due to twisting misaligned rows. If twisted while not fully aligned, it may cause the pieces diagonal to the corners to almost fully come out. It is simply fixed by turning the face back to where it was, causing the piece to go back to its original position. Excessive force may cause the colored tile to break off completely. In such a case, the cubelet will stay in place, yet the color would be gone. Rubiks Cube being speedsolved. ...

Solution

People able to rapidly solve puzzles like this usually favor the strategy of grouping similar edge pieces into solid strips, and centers into one-colored blocks. This allows the cube to be quickly solved with the same methods one would use for a 3×3×3 cube.

Another frequently used strategy is to solve the edges of the cube first. The corners can be placed just as they are in any previous order of cube puzzle, and the centers are manipulated with an algorithm similar to the one used in the 4×4×4 cube.

Records

The current world record for solving the Professor's Cube in an official competition is 1:44.47, set by Frederick Badie at the Belgian Open 2007 competition in Brussels. Takayuki Ookusa holds the record of 1:51.37 for the mean of five solves, set at the Osaka 2007 competition in Osaka, Japan. Mátyás Kuti holds the world record for solving the Professor's Cube while blindfolded, with a time of 10:05.16 set at the Czech Open 2007 competition.

See also

• Pocket Cube - A 2×2×2 version of the puzzle
• Rubik's Cube - The original 3×3×3 version of this puzzle
• Rubik's Revenge - A 4×4×4 version of the puzzle

Solved Pocket Cube Scrambled Pocket Cube Pocket Cube with one side tilted The Pocket Cube is the 2×2×2 equivalent of a Rubiks cube. ... Variations of Rubiks Cubes (from left to right: Rubiks Revenge, Rubiks Cube, Professors Cube, & Pocket Cube) Rubiks Cube (commonly misspelled rubix, rubicks or rubics cube) is a mechanical puzzle invented in 1974[1] by the Hungarian sculptor and professor of architecture Ernő Rubik. ... Rubiks Revenge in solved state The Rubiks Revenge is the 4×4×4 version of Rubiks Cube. ...

External links

• How to solve Professor's Cube
• Professor's Cube text solution
• Professor's Cube interactive solution
• Interesting patterns with various cubes
• Pretty Patterns A collection of pretty patterns for Rubik's Professor Cube
• An online version
• http://www.ganpuzzle.com/vcube555.htm Solve with 5 Simple Tricks. Interactive step by step animation preceded by detail descriptions
• Rubik's Solver A Java applet that solves the cube with animation using a corner first approach which works for cubes of any degree
• Program Rubik's Cube 3D Unlimited size