Currently, there is a rapid development of artificial intelligence systems that can solve and explain the solution of mathematical problems in the same way as students do. The problem of organizing interaction of artificial and human intelligence which does not lead to the degradation of the student's thinking skills arises. The article proposes one of the ways to solve this issue through the use of systems such as "smart problems" using the example of a support system for a combinatorics course. In this system, the student sets problems and solves them himself without the help of a computer, but the system can check the solutions to problems without simulating human reasoning. Such a system cannot replace a person, but it becomes an intelligent interlocutor when setting and solving problems. Thus, the task of formulating a problem shows the way to bypass the gap formed with the advent of artificial intelligence.