HTR 2x2x2 solver

[bcube]

Hi,

inspiration. Below are some thoughts about computer 2x2x2 solvers using the <U, R, F> move set and half-turn metric.

As shown earlier, Herbert Kociemba´s two-phase algorithm can be adapted to the 2x2x2 cube. By analyzing 2187 corner orientation cases, it can be shown that the worst case in phase 1 is 6 moves long, and by analyzing 2644 optimal 11-movers it can be shown the worst case in phase 2 is 11 moves long.

Moving on to Michael Feather´s two-phase algorithm and its adaptation to the 2x2x2 cube. By analyzying 2644 optimal 11-movers it can be shown the worst case in phase 1 is 10 moves long, and if exluding optimal half-turn 4-movers the worst case in phase 2 is 3 moves long.

The HTR 2x2x2 solver has currently some minor imperfections listed below but the basic idea is working:

• doesn't show '*' for optimal solutions, see help for how to find optimal solutions
• doesn't do 0+N, these will be 1+N
• doesn't reduce sequence for two sequential moves to same face - the solver will subsequently find the shorter solution except for when the length is at the specified Stop Len

 

[bcube]

Since the HTR 2x2x2 solver is technically a 3-color cube based solver, I thought I could share another 3-color cube based 2x2x2 solvers as well.

Starter solver is solving 2 opposite faces of 2 opposite colors, AKA phase 1 of 2-phase Kociemba´s algorithm adapted to the 2x2x2 cube.
3-color cube solver is solving phase 1 of the HTR solver without taking into account its phase 2 4-move restriction.

 

[bcube]

To complete the God's number count for beforementioned solvers, by analyzing 153090 cases of corners on a 3-color 3x3x3 cube (which is an equivalent to 25515 cases on a 3-color 2x2x2 cube with a fixed DBL corner if I did the math correctly) it can be shown that a 3-color 2x2x2 cube can be solved in at most 9 moves.