\problemdata      
        {?} % latex-friendly label for the prob.
        {Counting} % The topic(s) of the problem content.
        {?} % Source (if known)
        {Fall 2001, PS8} % Usage (list ones you are aware of).
        {Christos Kapoutsis, S02} % Last revision info (author, date).

\begin{problem}
The Towers of Hanoi game involves stacking $32$ disks onto three vertical
pegs, \cf Rosen \S 5.1, Example 5.  Each disk has a hole in the middle
through which a peg can slide, and all the disks have different diameters.
An arrangement of the disks on the pegs is allowed only if no disk rests
on a smaller disk.  How many different such arrangements are allowed?
  
\solution{There are $3^{32}$ different configurations by the product
rule: 3 choices of peg for the largest disk, 3 choices for the second
largest disk, and so on.}

\end{problem}