Greetings. I’m a professor in the Math/Stats department at Williams College. I began this webpage back in 1996, when I was a graduate student at Princeton. I ran many review sessions for a variety of undergraduate classes. Many of the students were interested in math riddles and brainteasers. I found these not only a great way to excite and motivate the students, but also a lot of fun!
I started collecting and posting riddles. My favorites are the ones that are related to key concepts in mathematics, where getting the solution shows you a new way of looking at the world. One of my favorites, and in fact the riddle that began the site, is C is for Cookie. It is possible to solve this by brute force, but it will be painful and time consuming. If you look at it the right way, you can do it in one line in your head. All you need to know is basic combinatorics (explicitly, n choose r).
I view many of these riddles as a wonderful tool to show students what is out there in mathematics. Too often high school and junior high school classes devolve into building (or trying to build) technical mastery. I agree basic skills are important, but they are not exciting. Doing 40 problems on the quadratic formula might make someone proficient, but it won’t make them passionate. My hope is that you will use these riddles to excite your students, to throw down the gauntlet and challenge them to think deeply.
Most, if not all, of these riddles have two very desirable properties: they have an elegant solution, and that solution doesn’t involve advanced mathematics. You don’t need calculus for these riddles; the most you need to know is some basic combinatorics in a few places. What you do need is some patience, and a willingness to explore. Don’t be afraid to try something — see where it leads!
It’s important to note that, just because advanced math isn’t used, this doesn’t make the riddles easy to solve. Far from it — often the less one needs to use, the harder it is to view the problem correctly. Students frequently have trouble in learning to create arguments and proofs; it is one thing to follow an argument line by line, and it is an entirely different skill to figure out for yourself what to do next. My hope is that by looking at a lot of these riddles and their solutions, you’ll build these and other skills, and see that math can be fun.
As time permits, I’ll write up some brief notes about how certain riddles and their solutions are connected to modern mathematics. Some are quite obvious, such as the cryptography problems like General Code. For others the connection is not at all apparent. My favorite in this regard is the Chess Problem, whose solution turns out to play a role in how airlines determine which planes fly which routes and when!
I have corresponded with numerous teachers at all levels over the years about using these riddles in the classroom. When I teach, I often find it creates a better atmosphere when I’m at the same level as my students, and thus it’s fine to give these riddles to your students before seeing the solution. Rest assured that if you and they have any questions, we’ll answer.
If you’re looking for some good ones to start, I suggest:
- Bridge Over Troubled Students
- C is for Cookie
- Safe Generals
- General Code
- Three Hats and a Strange Probability
- Mad as a Hatter
- Chess Problem
I don’t want to post what parts of modern math each is related to, as that can give a bit of a hint and spoil some of the fun of discovery.
I hope you enjoy the page. Please contact me and let me know how using these worked in your class, and if there is anything we can do to make that easier. I also encourage you to go to the Blog and write about using these in your class, and giving suggestions as to which riddles worked and which didn’t for your students.
PS: I’m often asked which riddles is the hardest; for me, it was You Light Up For Life.