100 people with 100 seats
Source:
December 9, 2011
combinatorics unsolvedcombinatorics
Problem Statement
There are people in a queue waiting to enter a hall. The hall has exactly seats numbered from to . The first person in the queue enters the hall, chooses any seat and sits there. The -th person in the queue, where can be , enters the hall after -th person is seated. He sits in seat number if he finds it vacant; otherwise he takes any unoccupied seat. Find the total number of ways in which seats can be filled up, provided the -th person occupies seat number .