Question

When eleven lines are drawn on a plane, with no three concurrent and no two parallel, how many open regions are produced?

Answer 1

Answer:

• 22

Step-by-step explanation:

We are considering for non-parallel lines and no three intersections

Let's see how many open areas are produced by the lines on a plane

• 1 line = 2 open areas
• 2 line = 4 open areas
• 3 lines = 6 open areas and 1 closed region
• 4 lines = 8 open areas and 3 closed regions
• 5 lines = 10 open areas and 6 closed regions

and so on

We see a pattern of 2n open areas for n lines, so

• 11 lines = 22 open areas