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How to Solve a 7x7x7 Rubik’s Cube
This puzzle is a cube which is built from smaller cubes, 7 to an edge, i.e. a 7×7×7 cube. Like a Rubik’s Cube each slice can rotate, which rearranges the small cubes on the surface of the puzzle.
The six sides of the cube are coloured, so every corner piece shows three colours, every edge piece shows 2 colours, and every face centre only one.
The number of positions: There are 8 corner pieces with 3 orientations each, 12 middle edge pieces with 2 orientations each, 24 inner edge pieces and 24 outer edge pieces apparently with 2 orientations each. There are 6 types of centre pieces, 24 pieces of each type. This gives a maximum of 8!·12!·24!8·38·260 positions. This limit is not reached because:
The total twist of the corners is fixed (3)
The total flip of the middle edges is fixed (2)
The permutation of the corners and middle edges is even (2)
The inner/outer edge orientation is dependent on its position, i.e. inner and outer edges cannot actually be flipped (248)
There are indistinguishable face centres (4!6·6)
This leaves 8!·12!·24! 8·37·210 / 4!36 = 19,500,551,183, 731,307,835,329,126, 754,019,748,794,904, 992,692,043,434,567, 152,132,912,323,232, 706,135,469,180,065, 278,712,755,853,360, 682,328,551,719,137, 311,299,993,600,000, 000,000,000,000,000, 000,000,000,000,000 = 1.95·10160 positions.
|No. of Pages||3|
|PDF Size||0.4 MB|
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