This year, I got to teach a Number Theory course during our Short Term, and for this blog post I want to write a bit about the experience, but mostly about the final project I gave my students, which was a cryptographic scavenger hunt. Before I begin, however, I should explain more about Bates. The academic year here consists of two twelve-week semesters (Fall and Winter) and one five-week Spring term. During the Short Terms (of which the students have to take at least two), students only take one course. This gives departments the opportunity of immersing their students in a particular topic. In the math department, for example, this is the term where we teach our intro to proofs class (a requirement for the major), affectionately known as Math Camp (or Math Boot Camp depending on who you ask). Other departments do a similar “methods” or “basics for the major” class, like History (known as History Hell), and Political Science (known as Politics Hell or Political Prison). As you can imagine, students have mixed feelings about these intense courses. Immersion is not always fun, especially if it means you are in class five hours a day, five days a week, writing and presenting proofs. I actually do think these courses work very well, and that students get a lot out of them (and I think going through the experience brings them closer together and helps with building the sense of community I’ve mentioned in previous posts).

Not all courses taught during Short Term are “basics” courses, however. This is also a great time to teach electives. We change ours from year to year (depending on who teaches it). The most popular one in recent years has been the Mathematics of Roller Coasters class, which even has a field trip on the last week of class. This year it was my turn, so I chose Number Theory (my area of expertise). I was pretty sure I wanted to run it very inquiry based, with group work, class presentations, and experimentation, and for the latter I wanted to use a computational component (they learned a bit of Sage). I also decided I would not give them exams, but rather weekly projects, similar in difficulty to a take-home exam but with the possibility of working together. I knew I wanted to finish with some Cryptography applications, since that is always very exciting to the students, and the issue was deciding what to give them as their final project. This is how I arrived at the Cryptography scavenger hunt idea.

Of course, for a while it was just an abstract “wouldn’t if be fun” kind of idea. I did a little research online and actually found a really great article by Judy and Eric Holdener describing their experience doing this at Kenyon College. It gave me a starting point, and most importantly, an idea of the timing for the activity. They had their students collect three clues and then decrypt a ciphertext which sent them to a library book, and the students finished in about 45 minutes. It also gave me the idea of giving the different teams the clues in different orders, so they wouldn’t converge on the same place at once. Since my class time was three hours, I decided to double their number of clues. We also learned RSA and ElGamal in class, so I had them use the two different cryptosystems. The last piece of my planning puzzle was inspired by one of my colleagues, Stephanie Kelley-Romano, from the Rhetoric department, who teaches a Short Term class in conspiracy theories. She does a “find the clues and bring down the conspiracy” activity in the last week of her class, and like her, I decided I would be kidnapped, and my students would rescue me using what they learned in our class.

On the day of the scavenger hunt, my students showed up to class and one of my colleagues delivered a ransom note. I had been kidnapped by some evildoers who watched too many episodes of Numb3rs and thought any number theory professor could crack any cryptosystem (this was inspired by the Season 1 episode called “Prime Suspect”, which we watched in class two weeks before). They were split into three teams, Alpha, Bravo and Charlie, and they had to rescue me before noon (class started at 9am). The first round of clues led them to three different professors (which gave them more clues), whose initials were R, S, and A. They decrypted and decoded the ciphertext using the clues (I will not go into the mathematics here), which turned out to be the call number for a library book (this idea is directly taken from the article by the Holdeners). In the book, they found a new clue, which led them to three more people and another ciphertext and set of clues. This one used ElGamal instead, and when they decrypted and decoded they found two numbers, which were the GPS coordinates for where I was being “held” (which turned out to be the Math and Statistics Workshop). The first team finished at about 11:15 (and they got prizes), the next two came in about ten minutes apart. They all found me, which was good. I did say that if by noon they hadn’t found me they could contact me through Skype. In fact, from the beginning they had a lifeline: they could contact me through Skype once if they got stuck (only the chat mode, not the video mode, since they could figure out where I was from the video).

Their reactions were mostly positive, although there were a couple of clues that really stumped them. The funny thing is, had they just googled the clues (exactly how I wrote them), they wouldn’t have been stumped. I didn’t try to make them easy, but I wanted the tricky part to be the math, not the clues. They were resourceful though, so even when Sage didn’t do what they wanted (they had trouble with the large exponents, even though we talked about it in class), they would use Wolfram Alpha or whatever they could think of for the computations. Overall, though, they thought it was really fun (one of them said “best final ever”), and I think it did what I wanted, which was evaluate some of the math they learned that last week in a way that was fun and different. It was a lot of prep work for me (especially the ordering of the clues and making sure everything was in its right place) but I didn’t have to do any grading (it’s impossible to grade something like this, so if you try this you’re sort of assuming everyone will get an A in one of the assignments, although I might have give a different grade to a team that didn’t find me in time, I think). I had a ton of fun planning and then chatting with them afterwards (a lot of them had lunch with me after), and I’m pretty sure they enjoyed it too.

So, dear readers, have you done something like this before? A friend of mine did something similar, but the final clue led them to their actual final exam, for example. Would you try this? Any ideas on other math classes were you could use a scavenger hunt format to test their knowledge? Does your school have a similar short term? If so, what cool classes have you been able to teach? Share your thoughts in the comments section below!

This sounds a lot like the stacks on Ditch Day at Caltech (except that

that’s 8 AM – 5 PM, which adds immensely to the prep time).

They’re made by the seniors to stump the underclassmen; the perfect

stack will take until 4:59 PM to be beaten.

My own (1991) was about knot theory. During the course of the day the people

involved would discover braids here and there. Before lunch, they got

a list of generators of the braid group, giving an enormously nonminimal

presentation of one of the braids. Then they were told to look in one

of the ovens, where they found a braid made of cookie dough, plus

instructions on how to cook it for dessert. Plus another twenty or so

ways of finding the five braids. (On five strands. Everything came

in fives.) The most time-consuming involved their following five trails

of colored stickers, each of which traced a way into the math building

(different entrances), then up the stairs, into the elevator, and so on,

finally out a different building, so the trails braided.

Subject to a couple additional constraints, there was a unique order to

multiply the braids to get the identity. That gave the combination

to the door. Inside was delicious braided mozzarella.

I taught a 100 level cryptography class for the first time recently, and I did three projects like this with my students. I broke them into groups of about 4 or 5 and they would have to solve a series of clues. They would have to do a little research sometimes, but then clues would send them around the campus. Various offices held packets of information for them and they would arrive, having decrypted the passcode — give the passcode and get the next clue. The eventual goals were a little different each time. One time they simply had to decrypt a song lyric (Stairway to Heaven) using a one-time pad and the clues led them to the pad. Another time, I hid cards from a Clue game around campus and each group had to find person, place, and weapon.

In another class, we talk about check digits and VINs and the like. I give them a series of veiled clues and they have to use them to find my car on campus. I leave something in the window for them to identify. They have to use check digits to find the correction to the VIN and a few other things to find the car. In that class also, we talk about Euler and Hamilton circuits and minimal spanning trees. I make them find such things using the campus.

Students have generally enjoyed the projects. I intend to expand the ones I do in cryptography in the fall.

Great activity! Lots of fun reading about it. Thanks.