Teaching algorithmic thinking enables students to use their knowledge in various contexts to reuse existing solutions to algorithmic problems. The aim of this study is to examine how students recognize which algorithmic concepts can be used in a new situation. We developed a card sorting task and investigated the ways in which secondary school students arranged algorithmic problems (Bebras tasks) into groups using algorithm as a criterion. Furthermore, we examined the students' explanations for their groupings. The results of this qualitative study indicate that students may recognize underlying algorithmic concepts directly or by identifying similarities with a previously solved problem; however, the direct recognition was more successful. Our findings also include the factors that play a role in students' recognition of algorithmic concepts, such as the degree of similarity to problems discussed during lessons. Our study highlights the significance of teaching students how to recognize the structure of algorithmic problems.