MathDB
Problems on 45 seat row of a movie theater

Source: Canadian Repêchage 2012: Problem 1

May 19, 2014
pigeonhole principlecombinatorics proposedcombinatorics

Problem Statement

The front row of a movie theatre contains 4545 seats.
[*] (a) If 4242 people are sitting in the front row, prove that there are 1010 consecutive seats that are all occupied.
[*] (b) Show that this conclusion doesn’t necessarily hold if only 4141 people are sitting in the front row.