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hello. im OFFICIALLY going on a break from blogging. but i might blog once in a while. and why, you might ask? im learning a new algorithm for solving the rubiks cube. its called the Roux. its difficult i tell you.
the rubiks cube is officially my drug. i cant stand a minnute without solving one! ask Sarah!
anyway, heres something that you should know about the Rubiks Cube. or not :P
The mathematics of the 3x3 Cube
As the centre pieces of each face of the Cube do not move, the total number of possible configurations is calculated by multiplying the number of possible arrangements of the corner pieces by the number of possible arrangements of edge pieces.
There are 8 corner pieces, so the number of possible arrangements equals 8! (or 8x7x6x5x4x3x2x1), which is 40320. Each corner piece has 3 different orientations, so this figure must be multiplied by 38 (3x3x3x3x3x3x3x3), which equals 6561. But when the Cube is almost complete, the number of possible moves diminishes, so the equation must be adjusted. In this case, once the second from last corner piece is placed, the last piece can have only one automatic orientation, so 6561 must be divided by 37, which is 2187. Finally, the total possible arrangements of corner pieces
40320 x 2187 = 88,179,840.
With the 12 Edge Pieces, the number of possible arrangements equals 12! (12x11x10…), which is 479,001,600. However, unlike corner pieces, it is impossible to exchange just two edge pieces, so once the third from last is placed, the remaining two can have only one possible arrangement, which means this figure must be divided by 2, leaving 239,500,800. Each edge piece has two different orientations, so this must now be multiplied by 212, which gives 6561. This figure must also be adjusted because once the third from last edge piece is placed, one of the remaining two can be reoriented but the last will always have a fixed orientation in relation to it. So 6561 must be divided by 211, which is 2048. Finally, the total possible arrangements of edge pieces
239,500,800 x 2048 = 490,497,638,400.
So the total possible arrangements of Rubik's Cube
88,179,840 x 490,497,638,400 = 43,252,003,274,489,856,000.
Or, to put it another way,
4.3 times 10 to the power of 19.
and a few facts:
- Rubik’s inspiration for the Cube’s internal mechanism came from pebbles in the River Danube whose edges had been smoothed away.
- Rubik called his invention the ‘Magic Cube’. It was renamed the Rubik’s Cube by the Ideal Toy Corporation in 1980.
- More than 300 million Rubik’s Cubes have been sold worldwide. If all the cubes were placed on top of each other they would reach the top of Mount Everest, twice!
- At the height of the Rubik’s craze in the mid-1980s, it was estimated that one-fifth of the world’s population had played the Cube.
- ‘Cubing’ still infects people of all ages. ‘Cubaholics’ are said to suffer from ‘Rubik's wrist’ and ‘Cubist's thumb’! ( this is something i am suffering from D: )
- There is also a dedicated art movement known as ‘Rubikubism’.
and here's a video to top it off :D ENJOY!
till here. Joel.
cheeerio.
scream here
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long post. [disregard this]
hello.
one minute and fifty two seconds.
blah.
i got tagged,
boring and exciting.
exams are finally over! :)
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