MathDB

9

Part of 2022 Moldova Team Selection Test

Problems(1)

Find all positive integers $n$, for which the grid always will cointain at least

Source: Moldova TST 2022

4/1/2022
Let nn be a positive integer. A grid of dimensions n×nn \times n is divided in n2n^2 1×11 \times 1 squares. Every segment of length 11 (side of a square) from this grid is coloured in blue or red. The number of red segments is not greater than n2n^2. Find all positive integers nn, for which the grid always will cointain at least one 1×11 \times 1 square which has at least three blue sides.
combinatorics