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 100 Dhs 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 100s arrived first then we would need to issue 50 IOUS. 1. What problem that you have seen in your pre-class work does this problem bear a resemblance to? 2. How can you use that analogous problem to give a geometric interpretation of sequences of arrivals of people with 50s and people with 100s that never require an IOU to be issued.

Fig: 1