$35 \cdot 33$ Six lines are in the same plane, no two lines are parallel, and no three lines are concurrent. Then the number of regions into which these six lines divide the plane is 
(A) 16.
(B) 20.
(C) 22.
(D) 24.
(E) 26.
(14th American High School Mathematics Examination, 1963)
[Solution] A straight line can divide a plane into 2 regions, which is $1+1$;
Adding a straight line (under the condition of the problem) makes the number of regions the plane is divided into equal to the sum of the number of regions before adding the line and the ordinal number of the line added, i.e., the maximum number of regions $n$ lines can divide a plane into is
$$
1+1+2+3+\cdots+n=\frac{n(n+1)}{2}+1 .
$$
When $n=6$, the value of the above expression is 22.
Therefore, the answer is $(C)$.