IMO 2013 Shortlist A2

Prove that in any set of 2000 distinct real numbers there exist two pairs a ą b and c ą d with a ‰ c or b ‰ d, such that...

imomathematicsolympiadshortlistalgebra

IMO 2013 Shortlist A2

Category: Algebra

Problem

Prove that in any set of 2000 distinct real numbers there exist two pairs a ą b and c ą d with a ‰ c or b ‰ d, such that ˇ ˇ ˇ ˇ a ´ b c ´ d ´ 1 ˇ ˇ ˇ ˇ ă . (Lithuania)