# Thistlethwaite's 63 move solution



## alwin5b (Mar 30, 2018)

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:

Orient edges and get them into their slices (18 moves)
Edges are then placed ( 9 moves)
Corners are done (36 moves)
By breaking up step 1 into the following substeps:

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
I found that step 1 only takes 16 moves at most, and more importantly it can easily be done without computer assistance and without memorization of any algorithms.

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?


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## Oatch (Mar 31, 2018)

As you mentioned, step 3 can be solved effectively using corner 3-cycles, and I'm fairly confident it can be done under 36 moves on average. Another plus is that such a solution is 100% intuitive (a whopping total of 0 algs!), since 3-cycles can be constructed using commutators. I've attached a number of examples to demonstrate this. Since after step 2 the edges are completely solved, I've used corner-only scrambles for my example solves.



Spoiler: Step 3 Examples



Example 1: 25 moves
Example 2: 24 moves
Example 3: 33 moves
Example 4: 32 moves
Example 5: 34 moves

Mean movecount of 5: *29.6 moves*



The general strategy is to solve two pieces at a time using 3-cycles (preferably pure comms , A9s, or orthogonals as required). Disjoint 2 cycles must be 'broken in to' by involving one of the pieces in a 3 cycle that simultaneously solves another random corner. Use a similar method to address twisted corners as the corner twist comm is relatively long compared to the 3-cycle comms (12/14 vs 8/9/10).

As for step 2, finding a solution within 9 moves eludes me for the moment, I will need to have a longer think about it. However, you could really consider the entire method to be a 2-phase solution, where you solve the edges in 27 moves (steps 1 + 2 combined), and the corners in 36 (step 3), and lose the restrictions imposed by the methodology of step 1. Perhaps you may find more luck with this added freedom.


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