You have n discs labeled 1,2,3,...,n (not necessarily in that order),
stacked one on top of each other (sort of like towers of hanoi).

The basic operation you can do on the stack is the following:
take some disc, and all the discs above it, and flip over that
part of the stack. For example, you can take the following
stack:

3
1
4
5
6
2
-

and, by applying the basic operation starting at disc 5, you can get

5
4
1
3
6
2
-

The problem has two parts:

(a) Show that, no matter how a stack of n discs starts out, by applying
the basic operation repeatedly, you can get the discs stacked in order
(1 on top, 2 next, ..., n on the bottom) using at most 2*n basic operations. 

(b) Show that, for any n, there is some way to order a stack of n discs
so that no matter how you apply the basic operations, at least n
basic operations are required to get the discs ordered. (In this part,
you have to specify a particular order that requires at least n basic
operations, AND you have to prove that there is no sequence of less
than n operations that orders the stack.)