2007 BMO Problems
Problems of the 2007 Balkan Mathematical Olympiad.
Let be a convex quadrilateral with , not equal to , and let be the intersection point of its diagonals. Prove that if and only if .
Find all functions such that
, for any .
Find all positive integers such that there exists a permutation on the set for which
is a rational number.
Note: A permutation of the set is a one-to-one function of this set to itself.
For a given positive integer , let be the boundaries of three convex -gons in the plane such that , , are finite. Find the maximum number of points in the set .