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A single line divides a plane into two regions. Two lines (by crossing) can divide a plane into four regions, three lines can divide it into seven regions. Let psubn be the max number of regions into which n lines divide a plane where n is a positive integer.

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Solution Summary

This shows how to find the max number of regions divided in a plane.

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In order for n lines to divide the plane into a maximum number of regions first any of the lines is parallel to another and no three of them intersect at the same point. Let R(n) ...

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