Explanation for the second example:
We are given one color wheel containing $12$ colors. Miss M has already chosen one color from the wheel (marked as number $1$ in the picture). Now she wants to choose $3$ more colors. Therefore, the sequence of her actions is as follows:
\begin{enumerate}
\item The maximum length of the sequence of unmarked colors is $11$. Therefore, we choose the color that will be in the middle and mark it with the number $2$.
\item Now we have sequences of $5$ and $5$ unmarked colors; we choose any and in the middle of the sequence, we select a color and mark it with the number $3$.
\item Among the sequences --- $2$, $2$, and $5$ we choose $5$ --- this is the maximum length of the sequence of unmarked colors before Miss M selects the $4$-th color.
\end{enumerate}


\begin{center}
  \includegraphics[scale=1.0]{problem_H.png} \\
  \small{The color wheel from the second example in the problem statement.}
\end{center}