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Let $n$ be a positive integer. A panel of dimenisions $2n\times2n$ is divided in

Source: Moldova TST 2021

September 19, 2021
combinatorics

Problem Statement

Let nn be a positive integer. A panel of dimenisions 2n×2n2n\times2n is divided in 4n24n^2 squares with dimensions 1×11\times1. What is the highest possible number of diagonals that can be drawn in 1×11\times1 squares, such that each two diagonals have no common points.
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