Collect Rubik's Cube? It is not difficult
The puzzle “Rubik's Cube” (“Magic Cube”, “Hungarian Cube” and even just “Rubik”) attracted attention, as they say, “of all population groups” and received the widest distribution. We have already written about the merits of this remarkable puzzle game, which schoolchildren and academics began to play with, finding in it dignities that match the level of scholarship, education, and inclination to research ( see Science and Life, No. 3, 1981 and No. 2, 1982 ) and even cited solution methods.
We will not touch either the mathematical theory of groups or quantum physics, for certain sections of which the Rubik's cube serves as an original visual aid. We will try to talk about how to put in order the tangled cube, and to those readers and readers who are very, very far from mathematics and from physics in general. Perhaps there will be some benefit in self-education, in broadening the horizons: after all, you will have to get acquainted with mathematical symbols and with drawings, although very simple ones. We hope that the desire to collect the cube will overpower their dislike for the exact sciences.
Therefore, we apologize in advance to more prepared readers for the “redundant” details in the description: there have already been a lot of letters asking “to tell so that it is clear to everyone, everyone ...”.
In square brackets [...] our explanations and hints are indicated.
First of all, let us recall the notation adopted in the journal. The faces of the cube are denoted by the letters F, T, P, L, B, H - the initial letters of the words Facade, Rear, Right, Left, Top, Bottom . Which facet of the cube to count as front - blue, green, etc. - depends on you and on the resulting situation.
In the process of assembling, you will have to take several times for the front of a particular edge, convenient for this case. The central cubes determine the color of the face, that is, we can say that even in a completely confused cube, the central cubes are already selected and it remains to attach 8 cubes of the same color to each of them.
The central cubes are denoted by one letter: f, n, l, t, t, n.
The edge cubes ( 12 pieces ) belong to two faces and are denoted by two letters, for example, fp, pv, fn , etc.
Corner cubes - in three letters by the name of faces, for example, FPV, FLN ...
The capital letters F, T, P, L, B, H denote the elementary operations of rotating the corresponding face (layer, slice) of the cube 90 ° clockwise .
The designations Ф < , Т < , П < , Л < , В < , Н < correspond to the rotation of the faces 90 ° counterclockwise.
The notation F 2 , P 2 , etc., speak of a double rotation of the corresponding face ( F 2 = FF ).
The letter C denotes the rotation of the middle layer .
Subscript shows from which side to make this turn. For example With p - from the right side, C n - from the bottom. C <L - from the left, counterclockwise, etc.
Record of the process (F < P < ) H 2 (PF) means: turn the front face counterclockwise 90 °, the same right side, turn the bottom face twice (that is, 180 °), turn the right side 90 ° ( clockwise), turn the front face.
Along with the alphabetic record of the processes, the matrix form of the record is also used, where the elementary operations are depicted by the drawing of the front face with the corresponding arrows indicating the directions of the turns of the corresponding face:
As a result of some operations, the central cubes leave their place - the cube changes its orientation. But, as you know, the color of the edge is usually determined by the color of the central cube. So that at the end of the task the orientation of the whole cube is the same as at the beginning, the operations of rotating the whole cube, denoted by the letter O , are introduced:
- O P - from the right side clockwise;
- O F - from the side of the facade face;
- About In - from the top face clockwise;
- О <П - from the right side counterclockwise;
- O <F - from the front face counterclockwise;
- O <B - from the side of the upper face counterclockwise;
We now turn to the actual assembly of the cube. There are several different systems, but we like the layered assembly best of all, when one layer is collected first, then the second and finally the third. A total of seven stages.
Cross top face
The desired cube is lowered down by turning the corresponding side face ( П, Т, Л ) and is displayed on the front face by the operation Н, Н < or Н 2
The operation of firing by a mirror rotation ( reverse ) of the same lateral face ends, restoring the original position of the affected edge cube of the upper layer.
After that, operation a) or b) of the first stage is carried out.
In case a), the cube went to the front face so that the color of its front face coincides with the color of the facade.
In case b) the cube must not only be moved up, but also deployed so that it is correctly oriented, taking its place.
On the [color] drawings,
dots mark [the arrows indicate] the place where the desired cube should be, which was previously displayed on the facade of the lower face.
Result: a cross of the upper face was assembled
The desired angular cube ( having the colors of the faces F, B, L ) is searched for and the same technique as described for the first stage is displayed in the left corner of your chosen front face.
There may be three cases of orientation of this cube. Compare your case with the picture and apply one of the operations of the second stage a) , b) or c) .
The dots mark [the arrows indicate] the place [on the upper face] , on which the desired cube should stand.
Find the remaining three corner cubes on the cube and repeat the described technique to move them to their places of the upper face [taking the front right, left, and back faces to alternate] .
Result: the top layer is selected.
The first two stages almost no one cause difficulties: it is quite easy to follow your actions, since all attention is paid to one layer, and what is being done in the two remaining ones is completely unimportant.
The processes shown in the figures are easily remembered if the mnemonic rule is applied. To move the cube left on the front face, to the left, the beginning of the process coincides with the initial letters NL - NaLevo , and to the right - with the initial letters NaRoyo .
And here, as you can see, the desired cube is found and first displayed down to the front face. If it is at the bottom - by simply turning the bottom face until it coincides with the color of the facade, and if it is in the middle belt, it must first be lowered down any of the operations a) or b) , and then combined in color with the color of the facade face and perform the operation of the third stage a) or b) .
Result: collected two layers.
The cross of the lower face [the initial designations of the faces - F, B, P in Fig. 6 are given for the current task, but it is assumed that the cube is inverted and its two upper layers, now below, have already been assembled] .
Operations that move the side cubes of the same face, which ultimately do not disturb the order of the collected layers, lead to the goal. One of the processes that allows you to pick up all the side cubes of an edge is given in the figure. It also shows what happens with the other cubes of the face.
Repeating the process, choosing a different facet, you can put in place all four dice.
Result: the edge cubes are in place, but, as a rule, two of them are incorrectly oriented.
Orientation of two onboard cubes according to D. Conway.
Very simple, easy to remember process, but it was here that some readers had difficulties. Here it is necessary to take into account: the deployed cube should be on the right side, in the figure  it is marked with arrows.
In figures a) , b) , and c) the possible cases of mis-oriented cubes (marked with dots) are presented. Using the general formula, in case a) it will be necessary to perform an intermediate turn B in order to bring the second die to the right edge, and in cases b) and c) , respectively, В < and В 2 .
Many were confused by the fact that after the first part of the process (PS n ), the 4 cube unfolded as it should, but the order in the assembled layers was disturbed. This was confusing and forced to throw an almost collected cube halfway through.
After completing the intermediate turn - not paying attention to the breakdown of the lower layers, - perform the operation (PS n ) 4 of the second part of the process, and everything will fall into place.
Result: the cross of the last layer is assembled.
It is possible to put the corners of the last face into place using (...) an 8-way [process] , convenient for memorizing, - a straight line, rearranging three corner cubes in a clockwise direction, and a reverse one, rearranging three cubes in a counterclockwise direction .
After the fifth stage, as a rule, at least one [angular] cubic will sit in its place, even if it is incorrectly oriented.
Turn the cube so that this cube is in the left far corner, and repeat the process once or twice until all the cubes fall into place.
Result: all the corner cubes took their places, but two of them ( and maybe four ) are not oriented correctly.
Orientation of corner cubes of the last face
The process is very easy to remember - it is a repeated sequence of turns PF < P < F .
Rotate the cube so that the cube you want to expand is in the upper right corner of the facade. The 8-way process ( 2 × 4 turns ) will turn it 1/3 turn clockwise . If the cube is still not oriented, repeat the 8-hodovka again ( in the formula this is reflected by the “n” index ).
Do not pay attention to the fact that the lower layers at the same time will come into disarray: the situation is similar to that done in the fifth stage, it is also a steam room, it is divided into two identical halves with an intermediate operation of turning the upper face. Performing the right side of the process automatically puts in order the broken harmony.
Figure  shows three cases of the location of "bad" cubes (they are marked with dots).
- intermediate turn B required
- turn in <
- turn in 2
Result: the last facet is collected.
Now it remains only to turn it and everything - the cube is assembled, clap your hands!
Here is a time-tested, old Soviet instruction. Then they were not mistaken and did not fool - this is an article from the magazine "Science and Life" from 1982.