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marked sqaures in a n x n sqaure grid

Source: 2007 Estonia National Olympiad Final Round grade 12 p5

March 12, 2020
combinatoricssquare table

Problem Statement

In a grid of dimensions n×nn \times n, a part of the squares is marked with crosses such that in each at least half of the 4×44 \times 4 squares are marked. Find the least possible the total number of marked squares in the grid.
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