Preparing children for safe behavior on the Internet is one of the most important tasks of secondary school, which is recognized at the state level. It is confirmed by the order of the Government of the Russian Federation of December 2, 2015 "Concept of Information Security of Children for 2018–2020" and the order of the Ministry of Digital Development, Communications and Mass Media of the Russian Federation of February 27, 2018 "On Approval of the Action Plan for the Implementation of the Concept of Information Security of Children for 2018–2020". The First Region Week of Cybersecurity was held as part of the implementation of this plan in October 2018 in the Arkhangelsk region. The article is devoted to the description of one of the events of this week — the contest of tasks on cybersecurity. The article presents the conceptual basis for the development of a system of competitive tasks, which were offered to schoolchildren of different classes of secondary school, and provides examples of problems with solutions. The authors of the article believe that the inclusion of such tasks in the content of school computer science textbooks will give teachers really effective tools to prepare schoolchildren for recognizing cyberthreats and the correct behavior when meeting with them.