Suppose you have a circular table of radius $R$. This table has been left outside, and it begins to rain at a constant rate of one droplet per second. The drops, which can be considered points as they fall, can only land in such a way such that they impact the surface of the table. Once they strike the table, they form a puddle of radius $r$, centered at their point of impact. What is the expected number of droplets it takes to cover the table in water?

The answer should be left in terms of $R$ and $r$. However, if you can simulate this, while changing both $r$ and $R$ so that some regression might be applied to find the approximate relation, that would be nice as well. I'd really like some intuition as to how the two are related. 

I have tried decomposing the problem by considering only the 1-dimensional case with line segments, but even its solution has eluded me. A potential starting point could be the discrete case of marbles falling into buckets. 

The following edit was suggested by [Jbeuh](https://math.stackexchange.com/users/36732/jbeuh): 

A more formal restatement of the problem :

Consider a sequence $X\_1,\ldots,X\_n$ of independent random variables following a uniform distribution on a disk $D$ of radius $R$. For each $i$, let $C\_i$ be the disk centered at $X\_i$ with radius $r$. Let $Y$ be the first $i$ such that the disks $C\_1,\ldots,C\_i$ forms a cover of $D$. What is the expected value of $Y$?