Floppy cube
The Floppycube is a rotating puzzle that is similar to the Rubik's Cube . Except that it is not 3 × 3 × 3, but only 3 × 3 × 1. It is thus cuboid .
How to play / solutions
Just like the classic Rubik's Cube, the Floppycube has 6 sides that have the same color when released. The aim is therefore to turn a floppy cube that has been twisted at will so that each side only has stickers that are all the same color.
Due to its mechanics, only 180 ° rotations of the front, the rear, the right and the left side are possible (if you hold the floppy cube in front of you as it is shown in the solved picture). From this it follows that it is impossible to turn one side only 90 ° and then simply tilt the corner stones that have been turned away. It is also not possible to rotate 2 lateral planes by 90 ° and then rotate the exposed edges individually.
There is a notation for the floppy cube so that the sequence of moves can be kept compact. F stands for the 180 ° rotation of the front side (for English front), B stands for the 180 ° rotation of the rear side (for English back), R stands for the 180 ° rotation of the right side (for English right) and L stands for the 180 ° rotation of the left side (for English left). A 180 ° rotation of the side between the right and the left is abbreviated as M (for middle layer), the 180 ° rotation of the side between the front and the back with S (for standing layer).
The floppy cube is one of the easiest rotating puzzles to solve. Often you can loosen the toy by turning it aimlessly. One of the most common techniques, on the other hand, is to first build a correct 2 × 2 × 1 block and then simply rotate the other 2 sides alternately until the cuboid is released.
Since the floppy cube is not a discipline in official speed cubing competitions, there is no official cube quick release record for this rotating puzzle.
mechanics
The floppy cube consists of a total of 9 stones of the same size. 1 center stone, 4 curb stones and 4 corner stones. These are covered with a total of 30 stickers in 6 colors.
Due to its mechanics, as already described in the section on how to play / solutions , only 180 ° rotations of the sides are possible. The curb stones are fixed to the center stone and can be rotated around their own axis. The corner stones, on the other hand, are not attached to the adjacent curb stones, but also to the center stone. But since a curb stone is just as big as the center stone, there would actually be no space for the attachment between the corner stone and the center stone. This problem was solved by the fact that the covers of the center stone can be easily bent so that there is still enough space between the center stone cover and the curb for the corner stone-center stone connection.
Mathematical properties
Possible positions
There are 4 edges in total. They can only ever be in the same position (1 ! ) And they can, however, have 2 different orientations (white above, yellow below or exactly the other way around) (this results in 2 4 possibilities).
Then there are the 4 corners. They can each be in one of the 4 positions (results in 4!), But their orientation cannot be determined additionally (1 4 ).
It follows that the floppy cube 1! × 2 4 × 4! × 1 4 = 384 positions, but only if disassembling and reassembling is allowed, namely not all positions can only be reached by turning. Such a position would be that only a single edge is tilted, but the rest of the floppy cube is correct. Ultimately, exactly half of these 384 positions are also possible, i.e. 384 ÷ 2 = 192 possible positions .
God's algorithm
As with several lighter Rubik's Cube, the minimum number of moves that you need to solve it from every position - the so-called God's algorithm - is known.
| required trains |
Positions |
|---|---|
| 0 | 1 |
| 1 | 4th |
| 2 | 10 |
| 3 | 24 |
| 4th | 53 |
| 5 | 64 |
| 6th | 31 |
| 7th | 3 |
| 8th | 1 |
| total | 192 |
In the position where a minimum of 8 moves are required to bring the floppy cube back into the released state, only all edges are misaligned, the corners and the center stone are completely correct. This situation, in which all edges are tilted, the rest of the Rubik's Cube is correct, is also known as a "super flip" and is one of the situations that take the longest to solve for many Rubik's Cubes is the 3 × 3 × 3 Rubik's Cube he also one of the positions that requires the longest currently found solution sequence.
Other mathematical features
However, the floppy cube has a special mathematical property. There is an algorithm , i.e. a certain sequence of individual moves, in which, when you execute this sequence of moves, you can see all possible positions of the floppy cube, each only once. If you started with a loosened floppy cube, you will get a loosened floppy cube after executing this sequence of moves. This means that if the floppy cube is twisted, you only have to carry out this sequence of moves and only have to look after each rotation to see whether the floppy cube is released. Logically, this sequence is 192 moves long and looks like this:
If you abbreviate the sequence of moves L FRFRFRFRFRF L FRFRFRFR L RFRFRFRFRFR L RFRFRFRFRFR L R , or in short: L 5 (FR) F L 4 (FR) L 5 (RF) R L 5 (RF) R L R with W , then this algorithm is WFWB WFWB .
variant
There was also a 2 × 3 × 3 cuboid: Rubik's Magical Domino, consisting of 18 individual cubes.