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Finite number of lines divide the plane in k regions

Source: ILL 1979 - Problem 58.

June 5, 2011
combinatorics unsolvedcombinatorics

Problem Statement

Prove that there exists a k0∈Nk_0\in\mathbb{N} such that for every k∈N,k>k0k\in\mathbb{N},k>k_0, there exists a finite number of lines in the plane not all parallel to one of them, that divide the plane exactly in kk regions. Find k0k_0.
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