[chrisshroba]

I used to be able to solve the 3x3 in high school using memorized algorithms and then I lost interest since there was no reasoning involved. Your comment makes me want to pick it back up and learn 3-style, so thank you for the clear explanation!

[vikingerik]

If what's fun is the reasoning, then the thing to do is other shapes and styles of puzzles besides the cube.

This is my collection: https://imgur.com/v9OuYNw

Like you, I learned the 3x3x3 in high school via memorized algorithms, and that was only so interesting. Years later my brother got me a Megaminx (the dodecahedron equivalent to the 3x3x3 cube, third one in the top row there) and I was absolutely fascinated by learning to solve that by porting what I knew from the cube. From there I got all those other shapes as well. The most interesting ones to search by name: Dayan Gem 3 (the one that looks like the Star of David), Face-Turning Octahedron (last one in the second row), Helicopter Cube (to the right of the 3x3x4), Rex Cube (right from the Helicopter Cube).

[billmcneale]

Even with CFOP, there is a large amount of intuition needed in order to break below the 25 second limit, mostly because of lookahead. During that phase, you need to train your fingers to do moves while your brain anticipates the next moves. There are no real formulas involved, it's really about intuition, pure skill, and multitasking.

I have hit a wall there personally.