$35 \cdot 39$ A line divides a plane into two parts, two lines can divide a plane into a maximum of four parts. If five lines can divide a plane into a maximum of $n$ parts, then $n$ equals
(A) 32.
(B) 31.
(C) 24.
(D) 18.
(E) 16.
(China Beijing Junior High School Mathematics Competition, 1984)
[Solution] Only when any two lines are not parallel and any three lines do not intersect at the same point can the plane be divided into the maximum number of parts.

It is easy to verify that three lines can divide a plane into a maximum of seven parts. The fourth line, intersecting with the first three, is divided into “four segments,” thus the number of parts divided by four lines is four more than that divided by three lines, which is $7+4=11$ parts.
Similarly, it can be deduced that five lines can divide a plane into a maximum of $11+5=16$ parts. Therefore, the answer is $(E)$.