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Marking cells on a board

Source: Baltic Way 2014, Problem 9

November 11, 2014
combinatorics proposedcombinatorics

Problem Statement

What is the least posssible number of cells that can be marked on an n×nn \times n board such that for each m>n2m >\frac{ n}{2} both diagonals of any m×mm \times m sub-board contain a marked cell?
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