Before Morwen B. Thistlethwaite came up with his famous 52 move computer algorithm in July 1981, the best known method, also found by Thistlethwaite, was a 63 move solution. The only information I could find about this method is that it consists of these 3 steps:
This made me wonder if the whole 63 move solution can be done without computer assistance. I suspect that you could use corner 3-cycles to solve step 3 efficiently, but I don't know how to do it in 36 moves.
So my question is: Is there a way to do steps 2 and 3 in 9 and 36 moves, without using a computer and without using more than, say, 20 algorithms?
- Orient edges and get them into their slices (18 moves)
- Edges are then placed ( 9 moves)
- Corners are done (36 moves)
- EOLine - would take 9 moves normally, but since the line can be made of any of the M slice edges and in any permutation, it only takes 8 moves
- put the other two M slice edges into the M slice - 4 moves
- E slice edges into E slice - 4 moves
This made me wonder if the whole 63 move solution can be done without computer assistance. I suspect that you could use corner 3-cycles to solve step 3 efficiently, but I don't know how to do it in 36 moves.
So my question is: Is there a way to do steps 2 and 3 in 9 and 36 moves, without using a computer and without using more than, say, 20 algorithms?