TITLE: How many cubes cover a bigger cube?
QUESTION [65 upvotes]: How many $n$-dimensional unit cubes
are needed to cover a cube with side
lengths $1+\epsilon$  for some
$\epsilon>0$?

For n=1, the answer is obviously two. For n=2, the drawing below shows that three unit cubes suffice, but it is impossible using only two cubes. In general, a total of $n+1$ cubes is enough, as is shown in Agol's answer, but is this the smallest number possible?

(source: folk.uio.no)

REPLY [4 votes]: I had this very same question posted on my web page http://webhome.auburn.edu/~kuperwl/ for more than 20 years. To the best of my knowledge, the complete answer is still unknown.