Problem: 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:
Answer Choices:
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E.
Solution:
Let be the number of lines and , the number of regions. It is not too difficult to discover the rule that . For . Hint: for one line there are two regions, that is, one more than the number of lines; note what happens to the regions when a line is added.