Cover a cicular hole with planks A friend of mine asked me the following question.


  Whats the minimum number of rectangular planks of unit
  width (and infinite length) needed to cover a circular hole with diameter $n$?


Obviously, $n$ is an upper bound because the hole can be covered by putting $n$ planks in parallel next to each other. Also it is easy to see that for small $n$, in particular $n=2$ and $n=3$ one cannot make do with fewer than $n$.

Is there a proof that in the general case $n$ planks are needed?
This is a theorem of Bang from 1950-51, solving Tarski's Plank Problem. See Wikipedia  for description and links.
How many pieces of unit width planks and infinite length are needed to cover a hole of diameter n?

Easy!

One piece :)

Just cut up each bit as required from that infinite length piece :)