A. 585. For some integer n2 each pair (i,j), where 1i,jn, is written on a card. We play the following game. The n2 cards are placed in an n×n table so that for every i and j, the card (i,j) is in the ith row, at the jth position. It is allowed to exchange the cards (i,j) and (k,l) if they are in the same row or in the same column, and i=k or j=l. Is it possible to reach that arrangement of the cards which contains (1,2) and (2,1) interchanged and all other cards are at their initial positions?
Based on the idea of Zoltán Bertalan, Békéscsaba
Deadline expired on 10 April 2013.