KöMaL - Középiskolai Matematikai és Fizikai Lapok
Sign In
Sign Up


Problem A. 585. (March 2013)

A. 585. For some integer n\ge2 each pair (i,j), where 1\lei,j\len, 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

(5 pont)

Deadline expired on April 10, 2013.


4 students sent a solution.
5 points:Ágoston Péter, Cyril Letrouit, Omer Cerrahoglu.
0 point:1 student.

Our web pages are supported by:   Ericsson   Cognex   Emberi Erőforrás Támogatáskezelő   Emberi Erőforrások Minisztériuma   Nemzeti Tehetség Program    
MTA Energiatudományi Kutatóközpont   MTA Wigner Fizikai Kutatóközpont     Nemzeti
Kulturális Alap   ELTE   Morgan Stanley