**A. 585.** For some integer *n*2 each pair (*i*,*j*), where 1*i*,*j**n*, is written on a card. We play the following game. The *n*^{2} cards are placed in an *n*×*n *table so that for every *i* and *j*, the card (*i*,*j*) is in the *i*th row, at the *j*th 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

(5 points)

**Deadline expired on 10 April 2013.**