81. Sports Problem (I). In a class, there are 25 students. Out of them, 17 can ride a bicycle, 13 can swim, and 8 can ski. No student masters all three sports, but both cyclists, swimmers, and skiers have good or satisfactory grades in mathematics, which is particularly noteworthy, as six students have unsatisfactory grades in this subject.

How many students have excellent grades in mathematics? How many swimmers can ski?
81. There are 25 students in the class. Since 6 students have unsatisfactory grades in mathematics, there are 19 students with grades at least satisfactory; there are no more than 19 athletes in the class. The number of "athlete-students" (if we count one sport practiced by one student as a unit) in the class is \(17+13+8=38\), and since no student practices all three sports at once, it follows that the total number of students practicing sports is 19, and each of them practices two sports simultaneously.

Now it is easy to answer the question posed in the problem.

a) No student in the class has an excellent grade in mathematics.

b) Out of the 19 athletes, 17 can ride a bicycle; therefore, only two students can swim and ski at the same time, which means that two swimmers can ski.