Professor's Cube

The Professor 's Cube is a mechanical puzzle in cube form. This is a 5 × 5 × 5 version of the Rubik 's Cube.

The aim of the game is such to produce a uniform color on each side of the cube, in other versions of the Rubik's Cube according to any rotation of all the parts.

Construction

The cube consists of a total of 98 parts:

• 8 corner pieces, each with three externally visible pages
• Edge portions 36 ( of which 12 internal and 24 external ) with two externally visible sides
• 54 middle portions ( of which 24 outer 24 and inner fixed 6 ) each having a visible outward side

Positions of the cube

In the Professor 's Cube corner pieces, edge pieces and middle parts can be moved for the most part independently. Therefore, for each of these component groups, the number of their possible positions are calculated separately.

The 8 corner pieces of the cube can be freely interchangeable, so there are a total of 8! Opportunities. Seven Corners can be respectively rotated in three different ways are (oriented). The orientation of the eighth corner arises from the orientation of the other seven, so there is for a total of 37 options.

The 24 outer edge parts can be interchanged to all types. These parts can not be re-oriented (rotated), since the shape of the component in the interior of the die is asymmetric. The orientation of an external edge portion is therefore unchangeable and it remains at 24! Possibilities for the outer edges of parts.

The 12 inner edge parts, however, can be reoriented (rotated) are. The orientation of 11 of these parts can be chosen freely, resulting in orientation of the last part. Furthermore, these 12 edge parts can be interchanged in all types, so that a total of 211 × 12 / result! 2 options. The division by 2 is performed, since the permutation of the corner pieces with the interchange of the inner edge portions related: The sum of Eckenvertauschungen and the inner Kantenvertauschungen can never be odd.

For the inner and outer parts of the center, there are 24 each! Vertauschungsmöglichkeiten. 4 as each of the parts of a color, and thus are indistinguishable, the number of possibilities by 4! 6 is divided. Therefore, the number of arrangements of the movable parts of the center ( 24! / ( 4! 6) ) 2

The calculations are multiplied together for each sub- groups give the total number of:

The Professor 's Cube has so 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 positions.

Solution

Some people who call themselves speedcubers are able to solve the Professor 's Cube and similar puzzles in a very short time. One of the known strategies, which is often used for all the blocks having larger dimensions than the 3 × 3 × 3, is that first of all the central and edge portions are arranged in color. Thereafter, the cubes are released only by rotating the outer rotary axes is equivalent to the 3 × 3 × 3 cubes.

World Records

The current world record for speed cubing for the Professor 's Cube is 51.09 seconds and was set up on the "Australian Nationals 2012" in Melbourne on 2 September 2012 by Feliks Zemdegs.

Feliks Zemdegs also holds the world record for average time when five-time solving the cube with 57.64 seconds. This record has been established also in the "Australian Nationals 2012".

Marcell Endrey achieved the world record for the Blind solving the cube in 6:44.77 minutes.