Solving the 4x4x4 using the Reduction Method
The Reduction Method is a method for solving big cubes. The
basic idea is to first solve all six centers to create one large center
on each face. Next, pair all edge pieces to create 12 large edges. At
this point, you can solve the puzzle like a 3x3. The only difference is
that on even cubes (such as the 4x4), there are a few "parity"
situations that cannot occur on a 3x3.
The first step is to solve the centers. This is a mostly intuitive
step, so the best way to improve at this step is to just practice.
In the second step, you'll pair the matching edges. I solve the edges
two at a time. It is possible to do this step with six edges at a time
or to do other things, but I won't get into that here. In general, this
step is pretty easy as it takes only a few moves to pair edges. The
toughest part in this step is the look-ahead to eliminate delays
In the third and final step, you'll solve the puzzle as a regular 3x3.
There are two parity algorithms that you need to learn, but other than
that, it's pretty standard.