CMIMC 2021 has ended! See the final results.

Math Contest Rules

### How to join the contest

On the contest date (February 27th), go to the contests page and you should see each round of the math contest, with the divisions that you selected. When a round begins, click the blue 'Join' button. You'll see a list of problems, and can submit answers on the same page.

### TCS Round

This is a 90 minute test with 3 problems to be completed as a team. You can talk to your teammates over zoom, but no external tool is allowed.

• Communication within the team is permitted.
• Solutions should be hand-written, and your hands must be visible on the camera during the contest.
• You can scan or take a picture of your solutions in the last 30 minutes of the 90-minute contest.
Solution format:
• Prepare to have some sort of scanning device or camera ready before the contest starts.
• Number all of the pages of the solution.
• The bound that is attempted to be proven must be stated clearly before each proof.
• Multiple bounds may be proven.
• Full points will be given for the best bound with a correct proof.
• Partial points will be awarded above that for incomplete proofs on higher bounds.
• Partial points will be deducted below that for holes in logic or rigor.
Proctoring
• Each team will be in their own Zoom breakout room.
• In Zoom, click on the “Ask for Help” feature to get assistance/clarification from a proctor. You will also be in a slack channel with your assigned proctor and may ask questions there, or ask your proctor to join your breakout room.
• Computational tools or looking up results is NOT PERMITTED.

### Team Round

This is a 60 minute test with 15 problems to be completed as a team. You can talk to your teammates over zoom, but no external tool is allowed.

During the 5-minute submission window at the end of the contest:

• You may discuss with your team members while submitting
• Anyone on your team can submit an answer, and the most recent submission will be used.
• We recommend that you prepare to also submit during the round so you get all your answers in. Teams should discuss and resolve conflicts BEFORE this window.
Proctoring
• Teams will be in their own zoom breakout room.
• In Zoom, click on the “Ask for Help” feature to get assistance/clarification from a proctor. You will also be in a slack channel with your assigned proctor and may ask questions there, or ask your proctor to join your breakout room.
• Computational tools or looking up results is NOT PERMITTED.

## Individual Rounds

There are three different rounds: Algebra and Number Theory, Combinatorics and Computer Science, and Geometry.

Each round has 8 problems which need to be solved in 60 minutes.

During the round NO communication with anyone will be allowed.

Divisions and Scoring
• Contestants may choose which division to participate in individually for all 3 subjects.
• Each problem will have a preset weight based on its position in the test (e.g. #1, #2). These weights will be adjusted by a factor based on the percentage of the contestants that solved each problem. For problems in division 1 only, we will assume no one in division 2 solves these problems. For problems in division 2 only, we will estimate how many division 1 contestants would solve these problems.
• The total sum of these values will be multiplied by 0.5 for division 2 contestants.
• Contestants will be given a 3-minute window at the end of each 60-minute block to submit their answers.
• After these 3 minutes, there will be no more writing/typing allowed.
• There will be a certain amount of allowed operations that you can use in your answers.
Proctoring
• All contestants will be in a general Zoom room (stay muted).
• Camera must be on and both hands/work area visible at essentially all times
• Please use the Zoom raise hand feature to ask a question, you may type once acknowledged by proctor.
• Otherwise, no interaction with keyboard/mouse/electronics allowed (including calculators). Computational tools or looking up results is NOT PERMITTED.

## Answer Format and Simplification Rules

For all short-answer tests (Team Round and Individual Rounds), you will be able to submit an arbitrary math expression as your answer. Try it out here!

Some common expressions you might need:

Example What to type
$a+b,\ a-b,\ a \cdot b,\ \dfrac{a}{b},\ a^b$ Addition: a+b, Subtraction: a-b, Multiplication: a*b, Division: a/b, Exponentiation: a^b
$\sqrt{x},\ \sqrt[n]{x}$ Square roots: sqrt x, $n^\text{th}$ roots: nthroot n x
$\ln x,\ \log x,\ \log_n x$ Natural (base $e$) logarithm: ln x, Base $10$ logarithm: log x, Base $n$ logarithm: log_n x
$\sin x,\ \cos x,\ \tan x$,
$\csc x,\ \sec x,\ \cot x$
Trig functions: sin x, cos x, tan x, csc x, sec x, cot x
$\dbinom{n}{k},\ n!$ Binomial coefficients: binom n k, Factorials: n!
$|x|$ Absolute value: |x|
$\pi,\ e$ Constants: pi, e

Your submitted answers will be automatically graded by a computer. In general, submissions that are mathematically equivalent to the correct answer will be considered correct. This means that for the following example problem:

Evaluate the sum $\displaystyle \sum_{i=0}^5 \binom{7}{i} \binom{8}{5-i}$.

answers such as $\binom{15}{5}$, $\frac{15!}{5! \cdot 10!}$, and $3003$ will all be considered correct.

All answers must be closed-form expressions, and there is a maximum submission length. This means that answers such as $\sum\limits_{i=0}^5 \binom{7}{i} \binom{8}{5-i}$ and $\binom{7}{0} \binom{8}{5} + \binom{7}{1} \binom{8}{4} + \binom{7}{2} \binom{8}{3} + \binom{7}{3} \binom{8}{2} + \binom{7}{4} \binom{8}{1} + \binom{7}{5} \binom{8}{0}$ will be marked as incorrect (the former is not closed-form, and the latter is too long).

You should try to simplify your answers as much as possible, but you don't need to worry about trivial simplifications like $\frac{1}{\sqrt{3}}$ vs $\frac{\sqrt{3}}{3}$. All reasonably simplified answers will be below the maximum submission length. If you believe that your submission was graded incorrectly, ask a CMIMC organizer on Slack and we will manually grade it.