If your goal is to solve (like 4x4, 5x5, 100x100) in Python:

Verified Python implementation of an N-dimensional Rubik's cube with rotation and integrity checking.

def _is_valid(self): """Verify that cube has correct number of each color piece.""" # Count each color cell counts = c: 0 for c in Color for face in self.faces.values(): for row in face: for color in row: counts[color] += 1 # Each color should appear exactly n*n times (one full face worth) # But centers are fixed only for odd n, and corners/edges fine. # Simple count check: each color appears n*n times for color in counts: if counts[color] != self.n * self.n: return False return True

: The algorithm does not solve the 39x39 directly. It uses a Reduction Method to turn it into a 3x3x3.

Creating a comprehensive guide on solving an nxnxn Rubik's Cube (where n can be any number, but typically refers to larger cubes beyond the standard 3x3x3) in under 39 seconds using a specific algorithm implemented in Python, and verified via GitHub, involves several steps. This guide will outline a general approach to solving large Rubik's Cubes efficiently, introduce a Python implementation, and point towards resources on GitHub for verification and further development.