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What is the maximum number of regions that the plane R2 can be partitioned into using 10 lines?

What is the maximum number of regions that the plane R2 can be partitioned into using 10 lines? Correct Answer 56

Key Points

The recurrence is given by A(n)=A(n−1)+n. Each new nth line drawn is creating n new partitions. While creating partitions, draw the new line in such a way that it cuts all the previously drawn n−1 lines, then the nth line will create n new partitions and previous A(n−1) partitions will remain the same. 

A(n)=A(n−1)+n. A(0)=1,A(1)=2,A(2)=4

A(10)=A(9)+10=46+10=56

A(9)=A(8)+9=37+9=46

A(8)=A(7)+8=29+8=37

A(7)=A(6)+7=22+7=29

A(6)=A(5)+6=16+6=22

A(5)=A(4)+5=11+5=16

A(4)=A(3)+4=7+4=11

A(3)=A(2)+3=4+3=7

Hence the correct answer is 56.

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