| Rubik's Cube |
Instructions
To scramble the puzzle press S on your keyboard.
To reset the puzzle press R on your keyboard
To rotate the cube hold the mouse down and drag while over the cubes middle section.
To move the side piece hold the mouse and drag, while over the side you want to rotate
Facts
Erno Rubik of Hungary invented the Magic Cube. Ideal Toys renamed it Rubik's Cube. Over 100 million Rubik's Cubes were sold in the period 1980-1982.
The centre pieces of each face are always in the same relationship to each other.
Therefore, the number of ways the other pieces can be arranged in relation to them (i.e. the possible arrangements of the cube) is:
Total possible arrangements = (possible arrangements of Corner Pieces) x (possible arrangements of Edge Pieces).
Possible Arrangements of Corner Pieces
There are 8 Corner Pieces. Therefore, the possible different arrangements of them is 8! (i.e. 8x7x6x5x4x3x2x1) = 40320.
Each Corner Piece has three different orientations, so this must then be multiplied by 3 to the power 8 (i.e. 3x3x3x3x3x3x3x3) which equals 6561.
However, with the actual cube, once the second from last Corner Piece is
placed, the last piece can have only one automatic orientation so this
should be divided by 3 (effectively 3 to the power 7) which equals 2187.
Thus, total possible arrangements of Corner Pieces = 40320 x 2187 = 88,179,840.
Possible Arrangements of Edge Pieces
There are 12 Edge Pieces. Therefore, the possible different arrangements of them is 12! (ie 12x11x10x9x8x7x6x5x4x3x2x1) = 479,001,600.
However, with the actual Cube (and 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, so this total must be divided by 2, which equals 239,500,800.
Each Edge Piece has two different orientations, so this must then be multiplied by 2 to the power 12 (i.e. 2x2x2x2x2x2x2x2x2x2x2x2) which equals 6561. However, with the actual cube, once the third from last Edge Piece is placed, although the last two pieces will be in fixed positions, one can be reoriented but the last will always have a fixed orientation in relation to it. So this must be divided by 2 (effectively 2 to the power 11) which equals 2048.
Thus, total possible arrangements of Edge Pieces = 239,500,800 x 2048 = 490,497,638,400.
So - Total Possible Arrangements of Rubik's Cube = (possible arrangements of Corner Pieces) x (possible arrangements of Edge Pieces) = 88,179,840 x 490,497,638,400 = 43,252,003,274,489,856,000.
One, and only one, of these possibilities presents the 'solved' Cube, having a single colour on each of its 6 sides. If you allow one second for each turn, it would take you 1400 million million years to go through ALL the possible configurations. In comparison, the whole universe is only 14 thousand million years old.