The Mathematical Olympiad is an international mathematics competition that takes place annually, attracting top students from over 90 countries. The competition is divided into two levels: the Junior Mathematical Olympiad (JMO) for students under 20 years old and the International Mathematical Olympiad (IMO) for students under 20 years old who have completed their secondary education.
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Problem (Combinatorics): Show any 6 points in a unit square contain two at distance ≤ 1/√2. Short solution: Partition square into 4 equal subsquares; by pigeonhole, some subsquare contains ≥2 points; max distance in subsquare is √(1/2)=1/√2. Geometry: Circle Inversion
Geometry: Circle Inversion