« Vrati se
Let K be a convex polygon in the plane and suppose that K is positioned in the coordinate system in such a way that
\text{area } (K \cap Q_i) =\frac 14  \text{area } K \  (i = 1, 2, 3, 4, ),
where the Q_i denote the quadrants of the plane. Prove that if K contains no nonzero lattice point, then the area of K is less than 4.

Slični zadaci

#NaslovOznakeRj.KvalitetaTežina
1981IMO Shortlist 1997 problem 250
1979IMO Shortlist 1997 problem 230
1972IMO Shortlist 1997 problem 160
1245IMO Shortlist 1966 problem 620
1153IMO Shortlist 1960 problem 71
1149IMO Shortlist 1960 problem 31