(a) It is known that among any group of the three students in a class two of them are friends. Total number of students is 25. Prove that there is a student who has at least 12 friends.
(b) There are 30 students in a class. They sit at 15 double desks, each one is for two students. Half of the girls sit with boys. Is it possible to make a rearrangement so that half of the boys sit with girls? Answered by Penny Nom.
From Amy: Four students drive to school in the same car. They claim they were late because they had a flat tire. Assuming they did not have a flat tire what is the probability that they all would choose the same tire if asked which one was flat. Answered by Stephen La Rocque.