Here’s a riddle that I thought about.

Question ⁇

Every year, 4 months before the start of a new semester each department in Queens College 🏫 releases the schedule of when classes are to be held and which professors will be teaching those classes.

You are the chair of the math department. You’ve assigned all but 2 professors to their classes. The two remaining professors can teach any class and both want to be full time employees. In order to be considered a full time professor you need to teach 6 hours a day and atleast one 2 hour class. The problem is that these two professors are married with little kids at home who need to be watched at all times. This means that both professors cannot teach at the same time (Because then nobody would be home). This also means that the moment one of them finishes teaching, they drive home (Luckly they have 2 cars 🚙). The contract you signed with them stipulates that you must pay for gas money incured by driving back and forth during school hours.

There are:

  • 2x 2 hours classes
  • 8x 1 hour classes

that need professors so you’ll need to divy those classes up among the 2 remaining professors. The way the schedule worked out this semester each of these classes are back-to-back with no breaks.

You want to minimize the amount you pay for gas so you want to schedule each professor for as many back-to-back classes as possible, having them switch shifts at home less often. You’d like to do an even split but the order in which the classes will occur is currently unknown and is decided by people not in your control.

Today is the final day to send the budget to the Budget Office 🏦. You want to add the necessary gas money, $1.00 a trip from the professor’s home to college and each trip requires both of the professors to drive one way ($2.00 total per switch), to the budget but don’t want to request more than necessary. On the other hand you don’t want to request less than necessary because then the gas money will be coming out of your pocket. How much money should you write down per day so that you won’t have to pay out of your pocket but you also wont be asking for more then you need.

Note: More then you need is anything over the guarenteed minimum, the guarenteed minimum means that although there could be scenarios where you pay less, this is the minimum you’d have to pay in the worst case.

Here is an example schedule:

7am - 8am 8 - 9 9 - 10 10 - 11 11am - 1pm 2 - 3 3 - 4 4 - 6 7 - 8 8 - 9
1hr class 1hr 1hr 1hr 2 hour 1hr 1hr 2 hour 1hr 1hr