Protoliths originate from a simple concept – picture yourself taking a walk where a coin is flipped with each step to dictate your direction; this is known as a random walk. In this intriguing journey, cubes traverse three dimensions. At each stage, one of the six possible faces is selected using a dice, determining the subsequent cube's position.
We present you with a collection of 9,900 protoliths. Can we expect to encounter two protoliths with the same shape among this vast array? Moreover, can you estimate the number of distinct shapes that coexist in this realm?
Let's think about these questions as we delve into the boundless realm of possibilities and nuances.