$36 \cdot 25$ A round table has exactly 60 chairs around it, and $N$ people are seated at the table in such a way that when one more person sits down, they must be adjacent to someone already seated. The smallest value that $N$ can take is
(A) 15 .
(B) 20 .
(C) 30 .
(D) 40 .
(E) 58 .
(42nd American High School Mathematics Examination, 1991)
[Solution 1] The $N$ people can be arranged as follows:
Among the 60 seats, place one person every three seats, totaling 20 people.

First, if another person sits down, they will inevitably be adjacent to one of the seated individuals; second, 20 cannot be reduced any further.
Therefore, the answer is $(B)$.
[Solution 2] Divide every 3 chairs into a group, with one person sitting in the middle chair, so that any additional person sitting down will definitely be adjacent to someone already seated.

Thus, 60 chairs can be divided into 20 groups, requiring only 20 people. Therefore, the answer is $(B)$.