In the 1980's there was a real hype when the mathematician Rubik invented
his 3×3×3 cube puzzle. Many similar puzzles have been invented
since. The 4×4×4 cube, for instance, was also somewhat popular.
The 5×5×5 cube is a real rarity. There is also a 2×2×2 cube.
The cube was the ideal activity during boring school lessons. To solve
the cube it was necessary to find move sequences (I call them tricks) which interchange
only a few cubis. This was the difficult part.
Once you have these tricks, the cube can easily be solved by suitably selecting and executing them.
Speed was then the criterium to compare one's skills.
The solution I found needed only 4 tricks (interchange 3 edges, interchange 3 vertices,
rotate 2 edges, rotate 3 vertices), all other tricks are mere shortcuts.
I extended this solution (by 2 more tricks) to the 4×4×4 cube
and realized that it also works for any n×n×n cube.
Some of my Rubik's Cubes
My Solution for all n×n×n Rubik's Cubes (Sketch)
With these tricks it is easy to figure out how to combine them and to solve all
n×n×n cubes. First solve all (n-2)×(n-2) centers,
then the edges and then the vertices, preferably layer by layer. Move 2
can easily be modified to interchange 3 edges of the final layer.
My shortcut tricks I'm keeping a secret ;-)
