When I was in high school geometry, we had a fun little game on the computer called Green Globs (the website for the software is http://www.greenglobs.net/index.html). A number of targets (globs) are randomly produced, and basically, the point of the game is to enter math equations to destroy targets in the least equations possible; writing an equation that intersects a glob means that it is destroyed. I haven't thought too much about this generalization but I thought it might be fun to examine, and I'm sure some work has been done in some field on a similar type question. The question I would eventually answer is the following :
"Let $R >0$ be a positive real number. Let $n >0$ be an integer. Fix some diameter $d
Given $R,n,d,w$ as above, what is the average number of lines of width $w$ necessary so that at least one line intersects each ball in at least one point?"
Now, I'm sure that in it's full generality as above, the question is quite hard. Perhaps examining specific cases are easier or have already been done. Do you know of any literature on this subject or something similiar?