MathDB

In an

n\times n

array all the fields are colored with a different color. In one move one can choose a row, move all the fields one place to the right, and move the last field (from the right) to the leftmost field of the row; or one can choose a column, move all the fields one place downwards, and move the field at the bottom of the column to the top field of the same column. For what values of

n

is it possible to reach any arrangement of the

n^2

fields using these kinds of steps?
Proposed by Ádám Schweitzer

Problem Statement