IMO 1992 LL PRK61

There are a board with 2n\cdot2n (= 4n2) squares and 4n2−1 cards

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IMO 1992 LL PRK61

Origin: PRK

Problem

There are a board with 2n\cdot2n (= 4n2) squares and 4n2−1 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?