MathDB
Linked rows and columns

Source: 239 MO 2024 J1

May 22, 2024
combinatoricsSets

Problem Statement

We will say that two sets of distinct numbers are <spanclass=latexitalic>linked</span><span class='latex-italic'>linked</span> to each other if between any two numbers of each set lies at least one number of the other set. Is it possible to fill the cells of a 100×200100 \times 200 rectangle with distinct numbers so that any two rows of the rectangle are linked to one another, and any two columns of the rectangle are linked to one another?