The spread of Artificial Intelligence (AI) has been recently generating worries among teachers and educators about the validity of assessment when students make use of AI tools to solve tasks. To tackle this issue, we propose mathematical problem solving activities to be carried out with the aid of ChatGPT, showing how problem solving and critical thinking continue to be pivotal in solving mathematical problems, even if this is performed with the aid of AI. After discussing theoretical frameworks on strategies of problem solving and phases of the critical thinking process, we present six problems of combinatorics that we submitted to ChatGPT. We also asked 40 university students to solve the six problems in group with the aid of ChatGPT during an international module on Problem Solving and Critical Thinking and collected the tutors' observations about the activities. Analyzing ChatGPT solutions and tutors' reflections, we show that the proposed activity requires problem solving and critical thinking to be accomplished. The results corroborate the idea that, instead of limiting the use of AI in education, it is possible to integrate it within learning and assessment to achieve the learning goals. [For the full proceedings, see ED636095.]