AI-powered education technologies can support students and teachers in computer science education. However, with the recent developments in generative AI, and especially the increasingly emerging popularity of ChatGPT, the effectiveness of using large language models for solving programming tasks has been underexplored. The present study examines ChatGPT's ability to generate code solutions at different difficulty levels for introductory programming courses. We conducted an experiment where ChatGPT was tested on 127 randomly selected programming problems provided by Kattis, an automatic software grading tool for computer science programs, often used in higher education. The results showed that ChatGPT independently could solve 19 out of 127 programming tasks generated and assessed by Kattis. Further, ChatGPT was found to be able to generate accurate code solutions for simple problems but encountered difficulties with more complex programming tasks. The results contribute to the ongoing debate on the utility of AI-powered tools in programming education.