2011 PUMaC Combinatorics A7 / B8
Source:
September 24, 2019
combinatorics
Problem Statement
At the start of the PUMaC opening ceremony in McCosh auditorium, the speaker counts people in the audience. Every minute afterwards, either one person enters the auditorium (due to waking up late) or leaves (in order to take a dreadful math contest). The speaker observes that in this time, exactly people enter the auditorium, leave, and was the largest audience size he saw. Find the largest integer such that divides the number of different possible sequences of entries and exits given the above information.