This case study aims to explore how high-achievers search the web for two different task types: easy vs. difficult. It took place in a science high school accepting students according to national exam scores. 10 voluntary students participated in the sessions. They were assigned two tasks with no time limitation. Screens were recorded and a researcher observed the whole session. The findings indicated that task type have an influence on shaping the web searching behavior. The difficult tasks may cause even high-achievers to get lost within the web. The copy-pasting behavior did not change with respect to task types. Such web pages as Wikipedia.org were very striking for students during both tasks. As the task got difficult, the number of tabs, keywords, visited pages, and duration became longer, besides frequent strategy change. The difficult task forced students to add their own explanations into the text since there was no ready-to-use information.