Question

在平面上画六条直线，其中任意两条都不平行，任意三条都不共点。它们把平面分成的区域数是：

Six straight lines are drawn in a plane with no two parallel and no three concurrent. The number of regions into which they divide the plane is:

$16$

$20$

$22$

$24$

$26$

第 $k$ 条直线被前面的直线截成 $k$ 段

The $k$ th line is cut into $k$ pieces by the previous lines

从一个区域开始，再加上 $1+2+\cdots+6$

Start with one region and add $1+2+\cdots+6$

依次画出的直线分别新增 $1,2,\ldots,6$ 个区域。因此区域总数为 $1+\sum_{k=1}^{6}k=1+21=22\text{。}$

所以正确答案是 C。

Successive lines create $1,2,\ldots,6$ new regions. Thus the total is $1+\sum_{k=1}^{6}k=1+21=22.$

Therefore, the correct answer is C.