Making a Rubik's Cube Example Work

My son is interested in being a speed cuber - someone who can solve the Rubik's cube fast. In fact, there are competitions to be won if you solve the cube in 30 seconds or less.  I believe he just wants to be amazing at something and this is something he can definitely amaze people with already!  

There are numerous ways to solve the cube, so I want to keep up with those sites for future reference.  Here is the list so far:

This has two important method descriptions.  One of the pages has Java enabled animations, which are not working in most browsers now.  So I want to repeat the portion of that site from the Waterman's Solution Method for Rubik's Cube - Stage III -- Starting about mid-page there is a section of animations that are failing on current browsers.  

Solve Redges in R Layer Cycle

There are two types of the R layer cycle that can occur depending on how many edges are in the cycle: 3-cycle and 4-cycle. Both cases are solved the same way using one of four sequences. The 3-cycles are easier to identify. If you identify one of the cycle types, you just have to find two edges in the cycle to position and orient correctly using a suitable sequence chosen from the sequences shown here. Since all sequences leaves all edges positioned in R layer in that layer, you can be sure that at least one of the remaining two redges will be positioned in R layer, which is the requirement of the next step.

R layer is temporarily held as the top layer in this step because the sequences are easier to perform then.

Solve Three Redges in Ring

If all four redges are in the ring we can use one of the following sequences to solve three edges in one step. All sequences are based on the same idea and can be understood intuitively. In particular, we solve two edges from the ring using a standard algorithm and at the right position in the sequence we insert another redge to the R layer.

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