what if: LoopOver Fewest Moves

P1: LoopOver/SwitchTile is https://loopover.xyz/

P2: Fewest Moves is an event where competitors attempt to solve a puzzle (almost always the 3x3x3) in as few moves as possible, starting from a given scramble.

Notation to help:

    A   B   C   D   E               C-
  ┌───┬───┬───┬───┬───┐	  ┌───┬───┬───┬───┬───┐	   ┌───┬───┬───┬───┬───┐
1 │ A │ B │ C │ D │ E │	  │   │   │↑ ↓│   │   │	   │   │   │   │   │   │
  ├───┼───┼───┼───┼───┤	  ├───┼───┼───┼───┼───┤	   ├───┼───┼───┼───┼───┤
2 │ F │ G │ H │ I │ J │	  │   │   │↑ ↓│   │   │	   │   │   │   │   │   │ 
  ├───┼───┼───┼───┼───┤	  ├───┼───┼───┼───┼───┤	   ├───┼───┼───┼───┼───┤
3 │ K │ L │ M │ N │ O │	  │   │   │↑ ↓│   │   │	3- │<->│<->│<->│<->│<->│ 3+
  ├───┼───┼───┼───┼───┤	  ├───┼───┼───┼───┼───┤	   ├───┼───┼───┼───┼───┤ 
4 │ P │ Q │ R │ S │ T │	  │   │   │↑ ↓│   │   │	   │   │   │   │   │   │ 
  ├───┼───┼───┼───┼───┤	  ├───┼───┼───┼───┼───┤	   ├───┼───┼───┼───┼───┤ 
5 │ U │ V │ W │ X │ Y │	  │   │   │↑ ↓│   │   │	   │   │   │   │   │   │
  └───┴───┴───┴───┴───┘	  └───┴───┴───┴───┴───┘	   └───┴───┴───┴───┴───┘ 
                                    C+
Column names (Excel)
A, B, C, ... , Y, Z, AA, AB, ..., AZ, BA, ... CA, ..., ZA, ZB, ..., ZZ, AAA, AAB, ... AZZ, BAA, ..., ZZZ, ...

Row names (Excel)
1, 2, 3, 4, ...

Multiple moves
3+ 3+ <=> 3+2
C- C- <=> C-2

Alternate form:
C+ <=> C	C- <=> C'
A+2 <=> A2	A-2 <=> A2'
3+2 <=> 3.2	3-2 <=> 3'2 <=> 3.2'

Move metrics

• SM (slide metric): any move of any rows/columns, by a single slide move, counts as 1 move (what the website uses)

• LM (line metric): any move of any rows/columns, by any multiples, counts as 1 move