Abstract
The article deals with the problem of forming plausible reasoning of students through open mathematical problems, justifies its necessity in preparing young people for real life.As a rule, in real life, the initial data are not always clearly formulated, the goal is not clearly set, and there are situations when there is not the only way out of this situation. Therefore, a person often faces open-type tasks. Open tasks are understood as tasks in which the initial data or the final goal are not clearly formulated. At the same time, students are to some extent given the freedom to set a task, choose a way of thinking and introduce additional parameters necessary for its solution. Within the framework of this study, a review of existing scientific literature, publications published in scientific journals was conducted, which necessitated the analysis of plausible reasoning among students, as well as the compilation and solution of open mathematical problems. The algorithm of actions for solving open problems and an example of identifying the possibili