
                  
\problemdata     
{S01-PS7-7}           
{counting}              
{} 		
{S01-PS7}
{S01 Karger}


%note: may be too hard. Problem doesn't have anyobvious shortcuts. 
%Tree method (brute force) is not very interesting.

\begin{problem}

 In Professor Karger's folk-dance class, dances are made of
four basic steps: a grapevine, a debka, a Yemenite, and a pivot.
There are some constraints:
\begin{itemize}
\item  A grapevine cannot follow a debka, and a debka cannot follow a
grapevine.  
\item A pivot cannot follow a Yemenite.  
\item Every dance must have at least one Yemenite
\end{itemize}
It \emph{is} permissible to repeat the same step multiple times, but
there must be at least 2 distinct steps in a dance.

How many distinct dances are there made up of a sequence of 4 basic
steps?

\solution{
93. Use a tree diagram to see this. 
}

\end{problem}                            










