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n-1 lines in nxn board

Source: Swedish Mathematical Competition 2004 p5

March 21, 2021
combinatorics

Problem Statement

A square of side n≥2n \ge 2 is divided into n2n^2 unit squares (n∈Nn \in N). One draws n−1n-1 lines so that the interior of each of the unit squares is cut by at least one of these lines. (a) Give an example of such a configuration for some nn. (b) Show that some two of the lines must meet inside the square.
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