We show that algorithmic thinking is a key ability in informatics that can be developed independently from learning programming. For this purpose we use problems that are not easy to solve but have an easily understandable problem definition. A proper visualization of these problems can help to understand the basic concepts connected with algorithms: correctness, termination, efficiency, determinism, parallelism, etc. The presented examples were used by the author in a pre-university course, they may also be used in secondary schools to help understanding some concepts of computer science.