First, let's divide the $5$ cells like this:
If you observe the colored cells (the non-black cells) upside-down:
The next thing is that, the $5$ cells are actually representing the binary. With black cell denoting $0$ and colored cells denoting $1$. (This refers to hint 2b.) But, it's not a regular binary. It's:
So, if we evaluate the numbers:
Yep, you ...
Meta: This is in effect a standard question in the theory of random walks. Does that make it off-topic as a textbook problem? I don't think so. The relevant meta-question is this one whose excellent and highest-voted answer gives this closely related question as an example of something that's a "math puzzle" rather than a "math problem".
OK then. Assuming ...