Challenging Mathematics by ``archimedes''

Đorđe Kadijević, Bogoljub Marinković

This paper presents the activities of the Serbian mathematical club ``Archimedes'' aiming at challenging mathematics in and beyond the classroom. It also summarizes main achievements of the club throughout three decades of its existence, focusing on the main findings from its rich experience in challenging mathematics. Examples of challenging tasks with some didactical remarks are given in the appendices.