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Rubic Toys

Posted by admin on August 26th, 2011

Rubic Toys
how is a Rubic Cube made?

Just wondering about the mechanics of the Rubic Cube Toy.

A standard Cube measures approximately 2¼ inches (5.7 cm) on each side. The puzzle consists of the twenty-six unique miniature cubes (“cubies”) on the surface. However, the centre cube of each face is merely a single square façade; all are affixed to the core mechanisms. These provide structure for the other pieces to fit into and rotate around. So there are twenty-one pieces: a single core piece consisting of three intersecting axes holding the six centre squares in place but letting them rotate, and twenty smaller plastic pieces which fit into it to form the assembled puzzle. The Cube can be taken apart without much difficulty, typically by turning one side through a 45° angle and prying an “edge cubie” away from a “centre cubie” until it dislodges (however, prying loose a corner cubie is a good way to break off a centre cubie – thus ruining the cube). It is a simple process to solve a Cube by taking it apart and reassembling it in a solved state; however, this is not the challenge.

There are twelve edge pieces which show two colored sides each, and eight corner pieces which show three colors. Each piece shows a unique color combination, but not all combinations are present (for example, there is no edge piece with both white and yellow sides, if white and yellow are on opposite sides of the solved Cube.). The location of these cubes relative to one another can be altered by twisting an outer third of the Cube 90°, 180° or 270°, but the location of the coloured sides relative to one another in the completed state of the puzzle cannot be altered: it is fixed by the relative positions of the centre squares and the distribution of colour combinations on edge and corner pieces.

For most recent Cubes, the colors of the stickers are red opposite orange, yellow opposite white, and green opposite blue. However, there also exist Cubes with alternative color arrangements. These alternative Cubes have the yellow face opposite the green, and the blue face opposite the white (with red and orange opposite faces remaining unchanged).

[edit] Permutations
A Normal (3x3x3) Rubik’s Cube can have (8! × 38−1) × (12! × 212−1)/2 = 43,252,003,274,489,856,000 different positions (permutations), or about 4.3 × 1019, forty-three quintillion (short scale) or forty-three trillion (long scale), but the puzzle is advertised as having only “billions” of positions, due to the general incomprehensibility of such a large number to laymen. Despite the vast number of positions, all Cubes can be solved in twenty-seven or fewer moves (see Optimal solutions for Rubik’s Cube).

In fact, there are (8! × 38) × (12! × 212) = 519,024,039,293,878,272,000 (about 519 quintillion on the short scale) possible arrangements of the pieces that make up the Cube, but only one in twelve of these is actually reachable. This is because there is no sequence of moves that will swap a single pair or rotate a single corner or edge cubie. Thus there are twelve possible sets of reachable configurations, sometimes called “universes” or “orbits,” into which the Cube can be placed by dismantling and reassembling it.

[edit] Centre faces
The original and still official Rubik’s Cube has no markings on the centre faces. This obscures the fact that the centre faces can rotate independently. If you have a marker pen, you could, for example, mark the central squares of an unshuffled Cube with four colored marks on each edge, each corresponding to the color of the adjacent square. Some Cubes have also been produced commercially with markings on all of the squares, such as the Lo Shu magic square or playing card suits. Thus one can scramble and then unscramble the Cube yet have the markings on the centres rotated, and it becomes an additional challenge to “solve” the centres as well.

Putting markings on the Rubik’s Cube increases the challenge chiefly because it expands the set of distinguishable possible configurations. When the Cube is unscrambled apart from the orientations of the central squares, there will always be an even number of squares requiring a quarter turn. Thus there are 46/2 = 2,048 possible configurations of the centre squares in the otherwise unscrambled position, increasing the total number of Cube permutation from 43,252,003,274,489,856,000 (43*1018)to 88,580,102,706,155,225,088,000 (89*1021), an increase of over 1000 times.

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