I was thinking about this problem, and have searched online to see if there has been work done on this, but have not found anything.
The question is if I wanted to divide a plane into n unique regions, what is the minimum number of lines needed? here's an illustration of what I mean
I did find the formula 0.5(n²+n+2) which gives the maximum number of spaces given a line n. While very related, it's almost the reverse of my question.
I did work on coming up with experimental values given here. There does seem to be a clear pattern, except for when n=5, which would throw the whole thing off.