【Analysis】There are $\left[\frac{50}{3}\right]=16$ students who are multiples of 3, and $\left[\frac{50}{7}\right]=7$ students who are multiples of 7. There are $\left[\frac{50}{3 \times 7}\right]=2$ students who are multiples of both 3 and 7. Therefore, there are $(16-2)+7-2=19$ students who turned around once, facing away from the teacher. The remaining 31 students either did not turn around or turned around twice, facing the teacher.
15. 50 students stand in a row facing the teacher. The teacher first asks everyone to report numbers from left to right as $1, 2, \cdots, 50$; then asks the students who report numbers that are multiples of 3 to turn around, and then asks the students who report numbers that are multiples of 7 to turn around. How many students are now facing the teacher?