There are 30 students attending a university award ceremony. Each student has a tag labeled by either A, B, or C. The tag is stick on the back of each student, which is visible only by the others except the student self. Students are not allowed to communicate each other. In other words, each student is aware of other students labels but not aware of his/her own label. Suppose there are 5 students with A, 10 students with B, and 15 students with C. During the ceremony, the university president announces that the award is given to students who have the label A, and asks the students to come to the podium to receive the award certificate. Explain how the students with A can figure out their label without communicating with other students and receive the certificate? Prove your solution by induction. Note: For this problem, it is assumed that students are aware that at least one student will receive the award certificate. After the announcement, the president will give maximum 30 chances to all students to figure out their own labels, with 1 minute for each chance. For example, the president will give the 1st minute to students to figure out their label, whoever figures out the own label with A will come to receive the certificate. If no one figures it out, the president will give a second chance (with 2nd minute), or continuing the third chance (3rd minute), fourth chance (4th minute), until thirtieth chance (30th minute) at maximum or stop at any round if all the students with A have figured it out and received the certificates.