Here is a complete, single-file HTML application for a 3x3 Rubik's Cube solver. It includes an intuitive visual color picker, an unfolded 2D cube layout with locked center pieces (to prevent illegal orientations), live color counters, and uses a Kociemba-based solver engine to find the shortest possible solution moves.
Save the code below as an `.html` file (e.g., `cube_solver.html`) and open it in any web browser.
```html
3x3 Rubik's Cube Solver
3x3 Rubik's Cube Solver
Orientation Guide: Hold your physical cube so that
Green is Facing You and
White is on Top. Match the configuration
below exactly as mapped out before hitting Solve. Centers are locked to guarantee proper alignment.