\problemdata     
{computation-1}           
{computation, robot, grid}              
{}              
{S02 in-class Week 5} 		
{S02 Meyer}        	


\begin{problem}
A robot moves on the two-dimensional integer grid.  It starts out at
$(0,0)$, and is allowed to move in any of these four ways:
\begin{enumerate}
\item (+2,-1)   Right 2, down 1
\item (-2,+1)   Left 2, up 1 
\item (+1,+3) 
\item (-1,-3) 
\end{enumerate}

Prove that this robot can never reach (1,1).

\solution{
A simple invariant that does the job is defined on states
$(i,j)$ by the predicate: $i + 2j$ is an integer multiple of $7$.
}
\end{problem}
