The ability of students to solve tasks is important for the development of their various skills. Students should be able to understand the information given, identify the critical features and their interrelationships, construct or apply an external representation, finally, take right decision for solving the task. Interest in contest essentially depends on tasks. Attraction, invention, tricks, surprise should be desirable features of each task presented to contest. The tasks have to be selected carefully, taking into account the different aspects of each task, i.e. what educational power it contains and how to interpret its’ attractiveness to students.