Professor's Cube

Professor's Cube in a state of chaos

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

As with other versions of the Rubik's Cube, the aim of the game is to create a uniform color by twisting all the parts on each side of the cube.

construction

The cube consists of a total of 98 parts:

• 8 corner parts, each with three outwardly visible sides
• 36 edge parts (of which 12 are inner and 24 are outer), each with two sides visible to the outside
• 54 middle parts (24 outer, 24 inner and 6 fixed) each with one side visible to the outside

Positions of the cube

All individual parts of a Professor's Cube

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

Corner pieces

The 8 corner parts of the cube can be interchanged as desired, so there are 8 in total! Options. Seven corners can each be rotated (oriented) in three different ways. The orientation of the eighth corner results from the orientation of the other seven, so that there are a total of 3 ⁷ possibilities.

Edge parts

The 24 outer edge parts can be exchanged in all ways. These parts cannot be reoriented (rotated) because the shape of the part inside the cube is asymmetrical. The orientation of an outer edge part cannot be changed and it remains at 24! Possibilities for the outer edge parts.

The 12 inner edge parts, however, can be reoriented (rotated). The orientation of 11 of these parts can be freely selected, which results in the orientation of the last part. Furthermore, these 12 edge parts can be exchanged in all ways, so that a total of 2 ¹¹ × 12! / 2 possibilities result. The division by 2 is carried out because the swapping of the corner parts is related to the swapping of the inner edge parts: The sum of the corner swaps and the inner edge swaps can never be odd.

Center parts

There are 24 each for the inner and outer center parts! Exchange possibilities. Since 4 of these parts are each of the same color and thus indistinguishable, the number of possibilities becomes 4! ⁶ divided. The number of arrangements of the movable center parts is therefore (24! / (4! ⁶ )) ² .

Total number

The calculations for the individual subgroups multiplied together give the total number:

${\displaystyle {\frac {8!\cdot 3^{7}\cdot 12!\cdot 2^{10}\cdot 24!^{3}}{4!^{12}}}\approx 2{,}83\cdot 10^{74}}$

The Professor's Cube has 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

Speedcubers are able to solve the Professor's Cube and similar puzzles in a very short time. One of the best-known strategies, which is often used for all cubes larger than the 3 × 3 × 3, is to first arrange the middle and edge parts by color. After that, the cube can be solved equivalent to the 3 × 3 × 3 cube simply by turning the outer axes of rotation.

World records

The current world record in speed cubing for the Professor's Cube is 34.92 seconds and was set by Max Park near Houston Winter 2020 .

The world record for the average time when solving the dice five times (the best and the worst of the five times are not included in the average) is held by Max Park with 39.65 seconds, set at the Western Championship 2019 .

Stanley Chapel set the world record in blindly solving the cube in 2: 21.62 minutes at the Michigan Cubing Club Epsilon 2019 .

Individual evidence

1. ^ Cubic Circular Issues 3 & 4 David Singmaster , 1982
2. ↑ World Cubing Association: Official 5 × 5 × 5 Single Results. Retrieved February 10, 2015 . 
3. ↑ World Cubing Association: Official 5 × 5 × 5 Average Results. Retrieved February 10, 2015 . 
4. ↑ World Cubing Association: Official 5 × 5 × 5 Blindfolded Single Results. Retrieved February 10, 2015 .