Searching a vector space (ish?)

Question

I come from a computer science background so please forgive any math transgressions I make.

I will try to describe what I'm looking for as best as I can.

I've been looking into methods of searching a vector space for a "target" of sorts but I have no idea where to start.

A simple version is searching RGB space for a "colour" ( I'm assuming the cardinality here is 3 right?). My idea is to present p number of options to a user. Each option is a different colour and they select the one closest to the colour they have in mind. Another set of options are presented closer to their target until they converge on the one they want.

I'm assuming that the target is itself a space since, in this case, the colours will become too similar for the user to tell apart. So as long as we end up in the target space we should be good.

So far, I think we have (again, feel free to correct me):

• Cardinality c
• Target space t
• Options presented p
• Number of options that need to be selected n to get to the target space

Now for my questions:

1. Is there a relationship between c, t, p and n?
2. Has any research been done into this sort of stuff and does it have a formal name?
3. For large value of c, I can image that values of p and n would also be quite large, but I'm assuming that I could reduce this by increasing t. Would this work?

Sorry again if this sounds like the ramblings of an idiot. Looking forward to any comments you have.

Many thanks in advance