Cubic magic variations refer to different ways in which the concept of magic cubes can be extended and modified. A magic cube is a three-dimensional arrangement of numbers in a cube shape where the sum of the numbers along each row, column, and diagonal is equal. These cubes have fascinated mathematicians and puzzle enthusiasts for centuries. One variation of cubic magic is the sequential magic cube. In this variation, instead of using a specific set of numbers, consecutive numbers from 1 to n³ are arranged in such a way that the sum of each row, column, and diagonal is equal to the same value. This variation adds an extra layer of challenge as it requires solving for unknown numbers and finding patterns within the cube.
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If you reach the last layer and one corner piece remains unsolved then go back to a triangle centre piece and rotate that so you can finish the solution of the Mastermorphix. If you reach the last layer and one corner piece remains unsolved then go back to a triangle centre piece and rotate that so you can finish the solution of the Mastermorphix.
This variation adds an extra layer of challenge as it requires solving for unknown numbers and finding patterns within the cube. Another variation is the even-odd magic cube. In this type of cube, the numbers are divided into two sets: even and odd numbers.
Rubik's Cube Shape Mods
In this section I will present some Rubik's Cube twisty puzzle shape mods which all have the classic 3x3x3 core mechanism in the inside but from outside they seem to be something else. These puzzles on the attached picture have all the same internal core mechanism, though they have different shapes and solutions.
To solve these you have to learn a new algorithm which rotates the centre pieces. On a classic cube you don't have to worry about the rotation of a centre piece because the faces have solid colours, but in these cases the centre piece can be textured.
Turn two centers 90 degrees at the same time:
F Clockwise, U Counterclockwise : ( M' U M U' ) x 5
F Counterclockwise, U Clockwise : ( M' U' M U ) x 5
To turn the U center 180 o : ( R U R' U ) x 5
Or do the T-Permutation twice:
( R U R' U' R' F R2 U' R' U' R U R' F' ) x 2
Mirror Cube
The Mirror Cube (or mirror blocks) is probably the most popular 3x3 variation out there. Reflective gold or silver stickers cover the pieces of this shape shifting cube. While on the classic Rubik's Cube six colours marked the solved state, in this case you can tell by shape and heights. A face is solved when it's flat and all pieces are on the same height with nothing sticking out. In solved position the distance between the core of the cube and the particular faces varies. Once you have found where a piece belongs you have to solve it the same way as the Rubik's Cube. There are 2x2x2 and 4x4x4 Mirror Cubes as well.
Ghost Cube
The Ghost Cube is an iconic and very difficlult shape shifter. In the solved state you have to first misalign the layers to make it fully functional. What makes it confusing at the first sight is that the solved state we want to achieve is not a cube, but a cube with the slightly shifted layers. It is recommended to familiarize yourself with this shape before scrambling it completely and trying to solve it.
Windmill Cube
The Windmill Cube is a 3x3 cube, but cut diagonally on the white and yellow faces, rather than horizontally like the rest of the cube. It is what is known as a supercube, which means that center rotation matters. So, what that means is that if one of the red, green, blue, or orange (on a windmill cube) centers are rotated by 90° in either direction or 180°, that would not be considered solved.
Fisher Cube
The Fisher Cube was made in the mid eighties by Tony Fisher and it was his first custom puzzle. Maybe this is the first Rubik's shape mod ever, so we're talking about a real classic. It has a perfect cube shape but basically it's a Rubik's Cube twisted 45 o around a central axis, making 4 edge pieces become centre pieces, 4 centre pieces become corner pieces and so on. If you can solve the classic 3x3x3 you can't have problems with this one, just pay attention to the parity.
Picture Cubes
Applying custom stickers on the cube can make it a new challenge. These cubes are known as picture cubes. This Earth Cube for example is not just a Rubik's Cube but some kind of jigsaw puzzle too, where you can put the pieces next to each other only if you have some serious geographic knowledge. Usually you have to orient the centre pieces if the stickers have patterns using the algorithm presented above.
YJ Heart Puzzle
A heart shaped Rubik's Cube can be a nice Valentines gift to a puzzle maniac. On the picture is a YJ Heart Puzzle, which has a very good quality, it moves smooth and is cheap (5$) and it doesn't have any stickers on it. The only annoying thing about it is because of the symmetric heart shape namely the opposite pieces are so similar in height and shape that you don't even know if you put a piece in the right spot or not. You need a microscope to distinguish two similar pieces. This little detail can make the whole puzzle hardly to enjoy.
Mastermorphix
The pillowed Mastermorphix is another classic 3x3x3 mod. There are 4-coloured and a 1-coloured versions too. This puzzle has 4 triangle shaped centre pieces (originally corners on the Rubik's Cube) which don't have to be oriented like all the other pieces. If you reach the last layer and one corner piece remains unsolved then go back to a triangle centre piece and rotate that so you can finish the solution of the Mastermorphix. Probably you will have to use the algorithm presented at the beginning of the page to rotate the last centre piece.
3x3x3 QJ Dodecahedron
This 14-sided puzzle has 2 pentagon and 12 trapezoidal faces. It is produced by QJ and it changes shape with every move. It's common with the classic 3x3x3 that you don't need to orient the centres. There are two triangle shaped corners which don't need to be oriented either. The interesting thing about it is that there are some four-coloured edge pieces. This puzzle is certainly a nice collection piece.
Axis Cube
The Axis Cube or also known as Axel Cube is a very intimidating looking mod when it is scrambled (as you can see on the first picture of this page). In solved position it is a cube, but it changes shape with every move. In this case you have to orient every single piece, there are no exceptions.
The cube is then arranged in a way that the sum of each row, column, and diagonal containing even numbers is equal to the sum of rows, columns, and diagonals containing odd numbers. This variation adds an element of symmetry and balance to the magic cube concept. There are also variations that involve using non-numeric elements in the cube arrangement. For example, alphabets or symbols can be used instead of numbers to create a symbol magic cube. The objective remains the same - arranging the symbols in such a way that the sum along each row, column, and diagonal is equal. This variation allows for more creative and artistic interpretations of the magic cube concept. Other variations of cubic magic involve changing the dimensions of the cube itself. For instance, a 4x4x4 magic cube requires arranging the numbers from 1 to 64 in a four-dimensional cube shape, ensuring that the sum of each row, column, diagonal, and 4D diagonal is equal. These higher-dimensional cubes pose an even greater challenge and require advanced mathematical techniques to solve. In conclusion, cubic magic variations expand upon the traditional concept of magic cubes by introducing different arrangements of numbers, using non-numeric elements, and exploring higher dimensions. These variations provide endless opportunities for puzzle solving and mathematical exploration..
Reviews for "Cubic Magic Variations: A Mathematical Perspective"
1. John - 2 stars - I found "Cubic magic variations" to be quite disappointing. The puzzles were repetitive and lacked innovation. The gameplay was slow and tedious, making it hard for me to stay engaged. The graphics and visuals were also underwhelming, lacking any captivating or immersive elements. Overall, I did not find this game enjoyable and would not recommend it to others.
2. Sarah - 3 stars - While "Cubic magic variations" had some interesting puzzle concepts, I felt that it fell short in execution. The controls were clunky and unintuitive, making it frustrating to navigate through the game. Additionally, I found the difficulty curve to be inconsistent, with some levels being too easy and others too challenging without a proper progression. The lack of a compelling story or narrative also made it difficult for me to stay invested. Although there were moments of enjoyment, I ultimately felt like there was room for improvement in various aspects of the game.
3. Mark - 2.5 stars - "Cubic magic variations" failed to capture my attention for long. The gameplay felt repetitive and lacked depth, with only slight variations in puzzles. The lack of creative level designs and objectives made it feel monotonous and uninspiring. Additionally, I encountered several technical glitches and bugs that hindered my overall experience. The potential was there, but the execution left much to be desired. I wouldn't highly recommend this game unless you're a die-hard fan of similar puzzle games.