Rubik's Revenge

Rubik's Revenge or Rubik's Master Cube is a cube-shaped puzzle. It is a slightly larger and more difficult variant of the Rubik 's Cube, also with six colors, but with three rather than two axes of rotation in any direction in space. Characterized the number of segments is increased at each of the six faces of nine 4 x 4 = 16

It acts as if the surface is divided into 56 cubes, the means of 90 - degree rotations alter the nine rotational axes, the position to each other. The aim of the game is patience, just as in the classic Rubik's Cube, to convert the master cube from a disordered position into its parent ground state, in which all segments of a side surface of the same color.

• 4.1 notation

• 6.1 introduction and instructions
• 6.2 Mathematics

History

The 4 × 4 × 4 version of the Rubik's Cube was founded in 1981 by the Hungarian mathematician Peter Sebesteny invented and patented. The rights of the patent he sold to the US-based Ideal Toy Company.

The axes, which hold together the cube and realize the rotating mechanism are split into four parts, and are held together by a core. The idea of ​​sharing the axes in this way was new and made ​​possible the grant of the patent.

Ideal Toy has four cubes marketed along with the " Rubik 's" trademark, sell it in the U.S. as " Rubik 's Revenge " and in Europe as " Rubik's Cube Master ". In the 1980s, the market was soon saturated with such different puzzle types that Ideal Toy after a few years ceased production of the four- cube. The implementation and marketing of other rotating mechanisms that were not patent protected, have ensured that the four - cube is manufactured and sold to date.

The world record in speed cubing holds the Australian Feliks Zemdegs with a time of 26.75 seconds, set at the "Australian Nationals 2012" in Melbourne on 2 September 2012.

Combinations

The Master Cube consists of 56 moving parts, which is significantly more than the 20 of the 3 × 3 × 3 cube. As with this, it is not a cube of which the surface is decomposed, but only by die segments. Specifically, these are:

Middle parts

• With one color, 24 pieces, four of each color
• The middle parts are not otherwise fixed as the classic Rubik's Cube, which is why the correct position of the stones must be checked at the quoins.
• The middle parts can be independently swapped positions, but there are four of each color, which can not be distinguished, one arrives at combinations of the middle parts.

Edge parts

• With two colors, 24 pieces, two per color combination
• The orientation of the edge parts is entirely dependent on their position in the cube. Although there are two pieces of each kind, they can not (erroneously ) to swap places since then also changes the orientation and the colors are exactly wrong.
• The edge parts can independently swap the positions, there is only one correct position and they can not change the orientation, which leads to combinations of the edge parts.

Corner pieces

• Three colors, eight of them, one per color combination
• The corner behave the same as that of the three - cube. You can swap the positions independently, and each corner has three different orientations, but influence each other: By design, only one-third of the theoretically possible combinations are accepted.
• Since the middle parts are movable, the master cube has as well as the Pocket Cube no fixed orientation in space: Any corner can always be regarded as correct and thus as a reference point on which the other solution is based.
• This leads to combinations of the corner pieces.

Overall, there are therefore

- many positions that the master cube can accept. These are far more than twice as many as the Rubik's Cube.

See also Combinatorics, Faculty

Difficulty

Although the Master Cube has a lot more possible positions than the three - cube, it is not difficult in itself. Of course, more stones have to be sorted, but as with rotation up to about 28.6 % of the parts to be moved, as opposed to 40% in the classic version, the parts affect each other less.

In particular, the middle parts can be sorted with short headways and easy. Any known solution strategy for the corner pieces can be used the same way the master cube. Unlike in the edge parts: Here are z.T. new headways needed because the behavior of individual edges stones has little correspondence in the three dice. Pairs, ie two edges stones next to each other, but can be sorted as well as individual stones at the edges of three cubes.

Solution strategies

Widely used is the approach to sort out the middle parts and to pair the edges. From now on, the average rotational axes are no longer used, whereby the master cube as the three - cube behaves. Any known strategy for this then also leads to the solution of the master cube, with two exceptions: It may happen that a pair of edges is oriented incorrectly. As shown above, then the two edge portions adjacent to swap the position, which only goes two middle parts, of which four are always the same, replace by the square. The second way is that two pairs of edges are reversed, which is not possible in normal 3x3 cubes.

There are also various other ways to solve the master cube.

Notation

A graphical notation is rarely used at the Rubik 's Revenge, widely used is a continuation of the letter notation. 90 degree rotations of the outer sides are denoted with capital letters as in the three - cube, according to their position front, back, top, bottom, left or right in a clockwise direction. According rotations are provided in a clockwise direction of the inside layers with small letters. Furthermore, means a counterclockwise rotation by 90 degrees and a 180 -degree rotation of the inner right level. Here, the direction refers to the level to rotate, while, for example, and have the same rotational orientation, it is between and reversed. Some refer to the lowercase letters but also a rotation of the outer and inner level, but this is usually indicated, as this is not the usual notation.

Comments

• It is possible, with the master cube (4 × 4 × 4) both the Pocket Cube to emulate ( 2 × 2 × 2 ) and the classic Rubik's Cube ( 3 × 3 × 3). In the first case, only the mean axes of rotation may be used, in the second only the two outer axes of rotation.
• The master cube can be disassembled and reassembled. This applies to the versions of all manufacturers, but for some this tool like a screwdriver is required. Also, sometimes need a few stickers to be removed to gain access to the mechanism.