Cubism Day 5

This stage is simple in principle - just flip the centre cubes so that the 'right colour' is on top. It is an easy process but because they flip in in pairs, it is easy to 'right' one cube and 'un-right' another. As a result of this, I find myself endlessly repeating the cycle and getting nowhere. I think the trick is to choose the first twist carefully.

What I find fascinating about the cube is that everything happens in pairs. There is some complex maths involving 3 dimensional matrices. I thought I might try explaining the maths here as simply as possible. Here goes ...

Imagine that all the individual cubes could be easily removed without physically damaging the Rubik's cube. If you move one piece, it must go somewhere else, thus displacing a second piece. That second piece must go somewhere too - the simplest place is where the first piece originally was. Although the Rubik's cube constrains the pieces so that they can't be easily physically removed, the same principle applies when effectively sliding squares around the outside surface of a cube. (The same principle actually also applies to those slider jigsaw puzzles as long as you consider the empty space as a 'piece'). Interestingly, if you were to physically remove ONE of the edge pieces, turn it upside down then replace it, the cube would be Impossible to solve. However, do this with TWO pieces, then it can still be solved.

If you want a simpler explanation of why they move in pairs, try this: they just do.