Question 103
At a secondary school, every class has an odd number of students. Furthermore, every student has a best friend (possibly from another class). Everyone is the best friend of his or her best friend. On the city trip, every student goes to Rome or Paris. Prove that the students can be divided over the two destinations such that
(i) every student goes on the city trip together with his best friend;
(ii) for every class the absolute difference between the number of students going to Rome and the number of students going to Paris equals 1.
(i) every student goes on the city trip together with his best friend;
(ii) for every class the absolute difference between the number of students going to Rome and the number of students going to Paris equals 1.