Abstract
What is the concept of the open-ended problem? Why is it necessary to pose open problems for research in the class? Which are the essential difficulties of treatment of the open problems in the class? How could we treat them? This text supplements a series of articles of the bibliography devoted to the resolution of the open problems. It presents short data of the practice and exposes many statements of the organized open problems of categories, favourable for research with groups of co-operation in the class with the level of the high school and senior high school. It brings new elements on the subject, and recalls for memory of the already treated questions.