MathDB

3

Part of 2024 Assara - South Russian Girl's MO

Problems(2)

Numbers in cells are modulo not more than 2024

Source: Assara 2024 J3

10/14/2024
In the cells of the 4×N4\times N table, integers are written, modulo no more than 20242024 (i.e. numbers from the set {−2024,−2023,…,−2,−1,0,1,2,3,…,2024}\{-2024, -2023,\dots , -2, -1, 0, 1, 2, 3,\dots , 2024\}) so that in each of the four lines there are no two equal numbers. At what maximum NN could it turn out that in each column the sum of the numbers is equal to 22? G.M.Sharafetdinova
combinatoricsabstract algebra
Numbers in cells are modulo not more than 2024; seniors version (2 to 23)

Source: Assara 2024 S3

10/14/2024
In the cells of the 4×N4\times N table, integers are written, modulo no more than 20242024 (i.e. numbers from the set {−2024,−2023,…,−2,−1,0,1,2,3,…,2024}\{-2024, -2023,\dots , -2, -1, 0, 1, 2, 3,\dots , 2024\}) so that in each of the four lines there are no two equal numbers. At what maximum NN could it turn out that in each column the sum of the numbers is equal to 2323? G.M.Sharafetdinova
combinatorics