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This book contains the most interesting problems from the first 24 years of the 'Mathematical Duel', an annual international mathematics competition between the students of four schools: the Gymnazium Mikulase Kopernika in Bilovec, Czech Republic, the Akademicki Zespol Szkol Ogolnoksztalcacych in Chorzow, Poland, the Bundesrealgymnasium Kepler in Graz, Austria and the Gymnazium Jakuba Skody in Prerov, Czech Republic.The problems are presented by topic, grouped under the headings Geometry, Combinatorics, Number Theory and Algebra, which is typical for olympiad-style competitions.Above all, it is of interest to students preparing for mathematics competitions as well as teachers looking for material to prepare their students, as well as mathematically interested enthusiasts from all walks of life looking for an intellectual challenge.