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Background: Geometry problems requiring auxiliary constructions are generally challenging for students, and they are traditionally included in Mathematics Olympiad tasks and examinations. Most teachers recommend that students remember basic auxiliary constructions, such as doubling the median of a triangle, inserting an additional circle, constructing the point of intersection of lines on which the segments lie, et?. These recommendations are usually insufficient for successful problem solving. Now students have a...

Background: Originality is the main specific feature of mathematical Olympiad problems. Formulating these problems requires a special kind of creativity and only a few people have this ability. They are called problem composers, and Rosen Nikolaev is one of them. H? creates mathematical tasks every day. More than 14 of them have been selected for the The National Student Olympiad in Mathematic and more than 40 for the Bulgarian Mathematical Olympiad. Such specialists are unique, not only because of their special a...

Background: Experimental mathematics is a new area of modern mathematics. The main feature of this field is obtaining mathematical results by means of computer experiments. Many facts show that statements of problems in the field of experimental mathematics are effective tool of teaching gifted students at school and university. The purpose of present paper is to show that using computer experiments generates some problems that should be solved as soon as possible. Methods: We obtained the list of these problems b...