Problem A. 404. (September 2006)
A. 404. The vertices of a regular 2ngon are . Call a diagonal V_{i}V_{j} even if i and j have the same parity. Dissect the polygon into triangles arbitrarily drawing 2n3 nonintersecting diagonals. The following operation is allowed on this dissection: Choose two vertices, V_{i} and V_{j}, which are either consecutive or they are connected by a diagonal used for the dissection. Then, on one side of the line V_{i}V_{j} replace each diagonal by its mirror image through the perpendicular bisector of V_{i}V_{j} (see the figure). Prove that, starting from an arbitrary dissection and applying this operation several times, it can be achieved that all even diagonals used for the dissection connect only vertices of even indices.
(Based on the sixth problem of the 47th IMO, Slovenia)
(5 pont)
Deadline expired on 16 October 2006.
Statistics:
21 students sent a solution.  
5 points:  Dobribán Edgár, Gyürke Csaba, Hujter Bálint, Károlyi Márton, KisfaludiBak Sándor, Korándi Dániel, Kornis Kristóf, Lovász László Miklós, Nagy 224 Csaba, Nagy 235 János, Nagy 314 Dániel, Szűcs 003 Gábor, Tomon István, Varga 171 László. 
4 points:  Dudás László, Fischer Richárd. 
3 points:  2 students. 
1 point:  1 student. 
0 point:  1 student. 
Unfair, not evaluated:  1 solution. 
