Unclear Directions
Darian is playing a board game on a large checkerboard that has been rotated by $45°$.
On each turn, he can move his counter one square in any of the eight compass directions shown: north ($N$), north-east ($NE$), east ($E$), south-east ($SE$), south ($S$), south-west ($SW$), west ($W$) and north-west ($NW$).
To keep track of his progress, Darian writes down each of the moves using the shortcuts above. Unfortunately, he forgets to put a space or comma between the symbols, so it’s not always clear exactly what the individual moves are.
In how many different squares could his counter finish with the following instructions?
\[\textbf{(a)}\ \text{NWNNNWEENW}\qquad\textbf{(b)}\ \text{NWNNWESENNWSE}\] \[\qquad\textbf{(c)}\ \text{NSNEWSNWEWSSWEN}\]Click to show my answers
$$ \textbf{(a)}\ 8\qquad\textbf{(b)}\ 32\qquad\textbf{(c)}\ 8 $$