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Which 3x3x3 positions require at least 20 moves to solve?

After barely getting my head around the concept, I have to say that the entire process itself is very fascinating.

If I am understanding this correctly, the computer, given a theoretical lookup table of all cube states, determines the shortest solution for a certain cube state not by having the optimal moves stored for each state, but instead, just storing a minimal detail of "what is the order the moves that should be done", not even the actual order, but just some "recognition" of which move is "next" to be closer to being solved.

It's like a proper thought process (quite similar to a human thought process, of "what should I do next"), without the actual details (i.e. algos) stored, but is able to "figure it out" (repeated lookups) via "experience" (i.e. the "mod" value). And the "building of the table" itself (gather the "optimal solve length" then just remembering "vague details" about it [the mod value], not the actual solve, and yet being able to use the small amount of data kept/learned to reconstruct a solve) sounds so much like actual "learning".

This is much closer to actual A.I. than anything I've ever seen.
I've seen programs that "learn" (e.g. OCR that is given lots of sample data to determine the scoring for certain "criteria" for recognizing characters), but have most of the actual "heavy lifting" done in the code. I am simply amazed how a simple table value of 0,1 or 2 and simple table lookups can simulate "thinking" and actually solve a cube optimally.
 
I think it's neat to illustrate the concept with a maze. Mark each cell of the grid with 0/1/2 and you can easily find the goal (on the bottom) from anywhere by going from 2 to 1, from 1 to 0, and from 0 to 2:
2195i5s.png

(basic image stolen from here)
 
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