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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: The question of safe use of the Internet by school students is one of the questions actively discussed in recent years. There is a particular concern about the entry of children into informal groups, sometimes of terrorist orientation, children's dependence on on-line-games, the treatment of the children to the sites, the content of which causes harm to physical and psychological health of children. Governments around the world have taken measures to ensure the safety of young Internet users at the leg...

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...