MathDB

1 to n^2 numbers on n x n table , same remainder by n in diff. rows + columns

Source: Tournament of Towns, Junior A-Level , Spring 2019 p5

May 13, 2020

square gridnumbers in a tabletablecombinatorics

Problem Statement

One needs to ffll the cells of an

n\times n

table (

n > 1

) with distinct integers from

1

n^2

so that every two consecutive integers are placed in cells that share a side, while every two integers with the same remainder if divided by

n

are placed in distinct rows and distinct columns. For which

n

is this possible?
(Alexandr Gribalko)