In the sixth, seventh, eighth, and ninth basketball games of the season, a player scored $23$,$14$, $11$, and $20$ points, respectively. Her points-per-game average was higher after nine games than it was after the first five games. If her average after ten games was greater than $18$, what is the least number of points she could have scored in the tenth game?
$\textbf{(A)}\ 26\qquad\textbf{(B)}\ 27\qquad\textbf{(C)}\ 28\qquad\textbf{(D)}\ 29\qquad\textbf{(E)}\ 30$
The sum of the scores for games $6$ through $9$ is $68$.  The average in these four games is $\frac{68}{4} = 17$.
The total points in all ten games is greater than $10\cdot 18 = 180$.  Thus, it must be at least $181$.
There are at least $181 - 68 = 113$ points in the other six games:  games $1-5$ and game $10$.
Games $1-5$ must have an average of less than $17$.  Thus we cannot put more than $16 + 17 + 17 + 17 + 17 = 84$ points in those five games.
Thus, the tenth game must have at least $113 - 84 = 29$ points, and the answer is $\boxed{D}$.