Ordered list of students
Source: 2020 Turkey TST P5
March 17, 2020
combinatorics
Problem Statement
There is at least one friend pair in a class of students with different names. Students in an ordered list of some of the students write the names of all their friends who are not currently written on the blackboard, in order. If each student on the list wrote at least one name on the board and the name of each student with at least one friend on the blackboard at the end of the process, call this list a . Prove that there exists a such that number of students in this list is even.