A circular table has 60 chairs around it. There are $N$ people seated at this table in such a way that the next person seated must sit next to someone. What is the smallest possible value for $N$?
$\text{(A) } 15\quad \text{(B) } 20\quad \text{(C) } 30\quad \text{(D) } 40\quad \text{(E) } 58$
$\fbox{B}$ If we fill every third chair with a person, then the condition is satisfied, giving $N=20$. Decreasing $N$ any further means there is at least one gap of $4$, so that the person can sit themselves in the middle (seat $2$ of $4$) and not be next to anyone. Hence the minimum value of $N$ is $20$.