There are 100 students taking an exam. The professor calls them one by one and asks each student a single person question: “How many of 100 students will have a “passed” mark by the end of this exam?” The students answer must be an integer. Upon receiving the answer, the professor immediately publicly announces the student’s mark which is either “passed” or “failed.”After all the students have got their marks, an inspector comes and checks if there is any student who gave the correct answer but got a “failed” mark. If at least one such student exists, then the professor is suspended and all the marks are replaced with “passed.” Otherwise no changes are made. Can the students come up with a strategy that guarantees a “passed” mark to each of them? Denis Afrizonov