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a grill of the shape of an n x n unit net by many metal bars of length 2

Source: ITAMO 2000 p5

January 25, 2020
gridminimumcombinatoricsTilingcombinatorial geometry

Problem Statement

A man disposes of sufficiently many metal bars of length 22 and wants to construct a grill of the shape of an n×nn \times n unit net. He is allowed to fold up two bars at an endpoint or to cut a bar into two equal pieces, but two bars may not overlap or intersect. What is the minimum number of pieces he must use?
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