It's Plane and Simple
Geometry
Level
pending
In a 2-D plane, where lines exist simply because they can, no lines are parallel, and no 3 lines are concurrent, how many regions are created by 20 lines?
2432902008176640000
1234567891011121314151617181920
211
210
400
21
22
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1 solution
Notice the pattern shown by the number of lines and the number of regions.
1 line = 2 regions
2 lines = 4 regions
3 lines = 7 regions
4 lines = 11 regions
For every n number of lines there is n th triangular number plus 1 regions. So 20 lines result in 20 times 21 divided by 2 = 210 + 1 = 2 1 1 .