Question $1$ of $5$

Problem $1$ Selling Tickets and Making Change

A university event requires a fifty dirham "donation" per attendee. Assume that every person who comes to the event pays with cash and each one has either a $50$

Dhs bill or a $100Dhs$ bill. The team that collects payment at the door neglected to get any small bills to be able to make change. If at least as many attendees pay

with $50$ as pay with $100$ then the ticket sellers will not have to issue anyone an "IOU" $($I owe you$)$ and send them their change later.

Suppose $2n$ people come to the event and every individual pays for their own "ticket" and that by the end of the evening there were exactly $n$ with $50$ Dhs notes

and exactly $n$ with $100$ Dhs notes. We want to think about different the implications of them arriving in different orders. For example, if all the people with $100$ s

arrived first then we would need to issue $50$ IOUs.

What problem that you have seen in your pre$-$class work does this problem bear a resemblance to$?$

How can you use that analogous problem to give a geometric interpretation of sequences of arrivals of people with $50$ s and people with $100$ s that never require an

IOU to be issued.