Everyone -– instructors and students –- want to make sure that grading of each test is fair, that the only thing that determines the students’ grade is their level of knowledge, that different students get the same penalty for the same mistake, irrespective of their gender, of their past grades, of their behavior in the class, of how many classes they missed, etc. How to help instructors achieve this goal? How to make sure that students are convinced that grading was indeed fair? In this paper, we describe possible measures: anonymous submissions, forming (and posting for all the student to see) an exact grading algorithm, and posting anonymized versions of all the solutions submitted by all the students. To implement these measures, it is necessary to have a centralized computer system that will generate random numbers or random emails for students to submit their tests –- but such a system is reasonably easy to design.