six straight lines are drawn in the plane such that no two lines are parallel and no three lines are concurrent. then the no of parts in which these lines divide are
Hint:
# parts with n+1 lines = # parts with n lines + ???
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The lines are non-parallel, non-concurrent.
If you have a single line, the line is undivided.
Total parts is 1.
A new line crosses the original line and is itself cut in 2 parts.
Total number of new parts is 3.
A new line crosses the previous two lines, creating 2 new parts on them,
while itself is crossed by both of those lines, so it has 3 parts.
Total number of new parts is 5.
A new line crosses all of the previous three lines, creating 3 new parts.
It is itself crossed by all three, so it has 4 parts.
Total number of new parts is 7.
There is a pattern to this.
Beginning with an original plane...
A new line divides the original plane. Add 1 to number of parts.
1 new line, 1 new part.
A new line cuts the previous line, adding 2 new parts.
2 lines, 2 new parts.
A new line cuts the 2 previous lines, adding 3 new parts.
3 lines, 3 new parts.
A new line cuts the 3 previous lines adding 4 new parts.
4 lines, 4 new parts.
etc.