The five (5) hottest members of the Innis Herald—Kiran, Julian, Bianca, Simba, and Ryan—are preparing holiday gift baskets for the rest of the team. Each of them purchases some materials; the details are organized in the table below.

Thus far, some members have spent more money than others—not ideal. The total cost of gift basket supplies is $200, so, to keep things fair, each person needs to have a net expenditure of $40 (= $200 / 5). Describe a sequence of transactions between members, after which everyone will have the same net expenditure of $40.

Consider using a spreadsheet or table to organize your work.

Figured it out? Try the following extensions:

1. Is there a sequence of four (4) transactions that accomplishes the goal? How about three (3) transactions?
2. What if Kiran is only able to pay Julian, Julian only Bianca, Bianca only Simba, Simba only Ryan, and Ryan only Kiran? Phrased differently, Kiran is unable to pay Bianca, Simba, or Ryan; Julian is unable to pay Simba, Ryan, or Kiran; and so on. (Perhaps there is some technical bug in the masthead’s favourite cash transfer app.) Under this restriction, can you still find a sequence of transactions that does the job?
3. Do the answers to these questions change if we change the costs in the table? What if we change the number of members?

Here’s a well-known contest math problem that is, surprisingly, tightly linked to extension 2:There are n gas stations along a circular road. The total amount of fuel at these stations is exactly the amount needed for a car to complete one loop. Show that there is a point on the road from where the car with an initially empty fuel tank can complete a loop.