MathDB
Good sets covering a table

Source: 239 MO 2024 S4

May 22, 2024
combinatorics

Problem Statement

Let nn be a positive integer greater than 11 and let us call an arbitrary set of cells in a n×nn\times n square <spanclass=′latex−italic′>good</span><span class='latex-italic'>good</span> if they are the intersection cells of several rows and several columns, such that none of those cells lie on the main diagonal. What is the minimum number of pairwise disjoint <spanclass=′latex−italic′>good</span><span class='latex-italic'>good</span> sets required to cover the entire table without the main diagonal?
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