Instructions

Important Information: New for 2026

This year, for each problem on the Quiz we're asking for three things:

  • the solution,
  • the scratchwork (see more below), and
  • a list of resources you used.

This means that you should do all of the following:

  1. Make an account for yourself on our portal at appsys.mathcamp.org right away.
  2. As you work on each separate problem, keep going back to appsys.mathcamp.org to upload your scratchwork frequently. We strongly recommend uploading your scratchwork as you go. We expect multiple uploads in different formats, and you don't have to worry about the filenames or upload order.
  3. Remember to keep track of the resources you use for each problem, along with a brief description of how you used it, and add them to the list we are asking for.

Documenting Your Scratchwork

For each problem, we are asking you to upload your scratchwork. This the stuff you put down while you were trying to understand the problem, trying different things, drawing pictures, making mistakes, making miscalculations, trying ideas that didn’t work, doodling, and eventually, perhaps by extremely roundabout and messy routes, working out the solution that you will eventually submit. We strongly encourage you to upload your scratchwork as you go! Return to appsys.mathcamp.org at any time and put your most recent work there.

We are not asking you change how you work out solutions. While working out the solution to a problem, you are going to pick up a pen or stylus or keyboard or marker anyway – in addition to all the work that goes on in your head. We are asking you to document and save your work (sheets of paper, notebooks, electronic notes, whiteboard notes, physical models), and we are asking you to take the time to scan and upload all of that. Don't worry about file names or the order; your uploads will be time-stamped and so we will know the order. Here's what to include:

  • If you are writing on paper, scan your notes and upload them. (Multiple-page pdfs are better than multiple photos, but photos are better than putting it off.)
  • If you use a whiteboard in a substantial way, take and add photos of your work.
  • If you wrote a program to work something out, please include that code.
  • Add photos of any physical models you made.
  • If you work electronically on a computer or a tablet, with either a keyboard or a stylus, please upload versions as you go. (And also save versions with big changes for yourself – trust us, this will be useful!! Uploads fail, things glitch, files get corrupted.) We understand that there will be erasing; we’re looking for a few major snapshots in time of your process. As a rule of thumb, save a version after a long work session.

We don’t expect your scratchwork to make sense. Please do not spend time on trying to make it make sense to a reader. We know what it’s like to do math! We are not asking you to do any extra writing or explaining of your work. We won’t worry about doodles and drawings, but if you wish you can black them out.

We also don’t expect your scratchwork to be 100% complete. We know you might have worked out a part of the solution with shower crayons. Or in your head while walking. That’s fine! We trust that eventually many of those ideas would have been put down in writing in some form. Some will remain unwritten, and that’s fine. Just collect for us the things you wrote down when you wrote them down.

Again, we encourage you to keep uploading your scratchwork frequently! Maybe every couple of days, maybe every time you've filled up 10 new sheets of paper. But even so, don’t recycle your papers in case there’s a technical issue and we need to ask for them later.

Before You Start: Policies on Getting Help

Before you begin the Quiz, make absolutely sure that you have read our policy on getting help on the Quiz. If in doubt about what is allowed, ask us!

(Our policy on getting help on the other parts of the application is here.)

General Instructions

We call it a Quiz, but it's really a challenge: a chance for you to show us how you approach new problems and new concepts in mathematics. What matters to us are not just your final results, but your reasoning. Correct answers on their own will count for very little: you have to justify all your assertions and prove to us that your solution is correct. (For some tips on writing proofs, see proof tips, or take a look at examples of solutions to past QQ problems.) Sometimes it may take a while to find the right way of approaching a problem. Be patient.

The problems are roughly in increasing order of difficulty, but even the later problems often have some easier parts. We don’t expect every applicant to solve every problem: in the past, we have sometimes admitted people who could do only half of them, occasionally even fewer. However, don’t just solve three or four problems and declare yourself done! The more problems you attempt, the better your chances. We strongly recommend that you try all the problems and send us the results of your investigations: partial solutions, conjectures, methods – everything counts. Also, if you come up with a solution that is messy and ugly, see if you can find a better way of thinking about the problem: elegance and clarity count too. None of the problems require a computer; you are welcome to write code as part of your solving process if you'd like, but first read a word of warning about programming.

If You Have a Clarifying Question

If you need clarification on any problem, please contact us. We almost always reply within 24 hours, usually much sooner. In addition to replying to your email: if we see the same clarification question several times, we will post the answer on the FAQ page.

Writing Up Your Solutions

You may handwrite or type your Quiz. For those interested in typing mathematics beautifully, we also offer you the LaTeX source file for the Qualifying Quiz. Please don't let it distract you from solving the problems, though! For more information on LaTeX, take a look at our LaTeX tutorial for the QQ. No matter how you write up your solutions, we require that you upload them with your application as PDF files; visit our PDF tutorial if you need help.

Finally: don't write your name on your Quiz. (Really!) Instead, write your applicant ID number on your Quiz. (You will receive an applicant ID number when you start your online application, on the welcome page.) Why not your name? When we grade Quizzes, we want to be thinking just about the math. So we're doing an experiment in which we evaluate all applicants just by ID number and then uncover the names later. We appreciate your help with the experiment.

Proceed forward to the Quiz problems. Good luck and have fun!