Question

2. Number Cards: There are 25 people sitting around a table, and each person has two cards. One of the numbers 1, 2, 3, , 25 is written on each card, and each number occurs on exactly two cards. At a signal, each person passes one of her cards the one with the smaller number to her right-hand neighbor. Prove that, sooner or later, one of the players will have two cards with the same numbers. 3. Airplane: Imagine there are a 100 people in line to board a plane that seats 100. The first person in line realizes he lost his boarding pass, so when he boards he decides to take a random seat instead. Every person that boards the plane after him will either take their "proper" seat, or, if that seat is taken, a random seat instead. What is the probability that the last person that boards will end up in his/her proper seat?

both

Answer 1