MathDB
JBMO TST Bosnia and Herzegovina P2

Source:

August 10, 2020
boardcombinatoricsnumbers

Problem Statement

A board n×nn \times n is divided into n2n^2 unit squares and a number is written in each unit square. Such a board is called interesting if the following conditions hold: ∘\circ In all unit squares below the main diagonal, the number 00 is written; ∘\circ Positive integers are written in all other unit squares. ∘\circ When we look at the sums in all nn rows, and the sums in all nn columns, those 2n2n numbers are actually the numbers 1,2,...,2n1,2,...,2n (not necessarily in that order).
a)a) Determine the largest number that can appear in a 6×66 \times 6 interesting board. b)b) Prove that there is no interesting board of dimensions 7×77\times 7.
Back to ProblemsView on AoPS