MathDB

There are a board with

2n \cdot 2n \ (= 4n^2)

squares and

4n^2-1

cards numbered with different natural numbers. These cards are put one by one on each of the squares. One square is empty. We can move a card to an empty square from one of the adjacent squares (two squares are adjacent if they have a common edge). Is it possible to exchange two cards on two adjacent squares of a column (or a row) in a finite number of movements?

Problem Statement