SJAM MATHLETES
presents
Second SJAM Mathematical Olympiad
Dec. 21, 2020, 12:00AM – Jan. 17, 2021, 11:59PM
Problem set
Official solutions
Results:
For participants: please check your email for feedback on your submission :)
This year we had 22 teams who signed up and 9 teams who made a submission before the deadline. The top 6 teams are listed below. (The scores in the parentheses indicate maximum possible scores.)
| Team name | School | Overall award | Division‑based award | Total score (78) | Q1 (1) | Q2 (2) | Q3 (3) | Q4 (4) | Q5 (5) | Q6 (6) | Q7 (7) | Q8 (8) | Q9 (9) | Q10 (10) | Q11 (11) | Q12 (12) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| I’d li‑ke so‑me mo‑re caw‑fee | UTokyo | Gold Award | Old People: Gold | 52.5 | 1 | 2 | 3 | 3.5 | 1 | 6 | 7 | 6.5 | 9 | 1.5 | 1 | 11 |
| Xiang | SJAM | Silver Award | Senior Level: Gold | 49.5 | 1 | 2 | 2.5 | 3.5 | 3 | 5 | 2 | 8 | 3 | 7.5 | 0 | 12 |
| REQUIRED | Laurelwood | Bronze Award | Babies: Gold | 36 | 1 | 2 | 3 | 3.5 | 5 | 6 | 2 | 7.5 | 6 | - | - | - |
| Potato | SJAM | Honorable Mention | Junior Level: Gold | 24 | 1 | 1.5 | 2 | 1 | 0 | 6 | 2 | 1.5 | 9 | - | - | - |
| Zed Li’s Knees | SJAM | Honorable Mention | Senior Level: Silver | 13.5 | 1 | 2 | 3 | 0 | 1.5 | 6 | - | - | - | - | - | - |
| Logic Flaw | SJAM | Honorable Mention | Junior Level: Silver | 11 | 0.5 | 2 | 2.5 | - | 0 | - | 2 | 4 | 0 | - | - | - |
Contact information:
If you have any questions or comments, please email Zed (liz0075@wrdsb.ca), Tian (chent4452@wrdsb.ca), or Biscuit (bichc3017@wrdsb.ca). We’ll be happy to help :D
Basic information:
- Number of intelligent beings per team: 3 or fewer (meaning you can have additional members on your team if they are extremely stupid, e.g., your dog/cat/
siblings) - Age restriction: NONE
- Knowledge NOT required to solve the problems: proof of the Riemann Hypothesis, proof that P=NP, proof of Goldbach’s conjecture, and other knowledge beyond the scope of the standard Gr. 12 Advanced Functions course. Exception: A few of the hardest problems may involve some standard math contest topics, which are readily available on Wikipedia.
Instructions:
TL;DR: Register, access the problems, and submit using the links above. Everything is super straightforward. You can’t get help from people outside your team. Please include your team name in the file name of each file you submit. HAVE FUN! ;D
- Cheating: No help from human beings outside your team is allowed. This means no whining to your mommy/daddy, no posting on discussion forums, etc. Exception: You’re allowed to use Wikipedia. (And other existing online sources too, although I doubt their credibility.)
- Registration: Click on the sign-up link above to sign your team up for the Olympiad any time before the submission deadline (Jan. 17 at 11:59PM). You may edit your registration information after you submit it up until the deadline.
- A cool team name will be required during registration.
Teams with boring names will be disqualified. - The grade level of the most aged member of your team will be required. This is to determine awards for different age groups:
- Babies: < Gr. 9
- Junior Level: Gr. 9/10
- Senior Level: Gr. 11/12 (including Cégep Year 1)
- Old People: > Gr. 12 (e.g., 5th year, Cégep Year 2)
- Note that members can be from different schools, though each team can only represent one school. The school your team represents must be attended by at least one team member (i.e., the coolest team member).
- A cool team name will be required during registration.
- Problems: Click on the link at the top of this page to access the problems, in case you missed the giant blue letters that’s impossible not to see.
- Mark breakdown: \(\sum_{k=1}^{12} k\)
- The problem difficulty is weakly positively correlated with the number of points it is out of
- Solution write-up and submission: Scroll up to access the submission link. You may edit your submission up until the deadline.
- Submissions will trivially be electronic. Allowed formats are PDF, documents, and images. Both handwriting the solutions and typing the solutions are accepted.
- Registration information provided in the submissions must match the information provided in the sign-up form.
- It is left as an exercise to the reader to show that the solution to each problem must be uploaded as separate files.
- Please include your team name in the file names of your submission.
- A complete and correct solution is required for full marks on a problem.
- Scoring: Your mark will be of the form of \(a + bi\) (\(a\), \(b\) are real numbers and \(i\) satisfies \(i^2 = -1\)), which is determined as follows:
- \(a\) (\(0 \leq a \leq \sum_{k=1}^{12} k \)) will be based on the mathematical rigor, completeness, and clarity of your solutions
and the coolness of your team name- If your solution matches one of the official solutions, we’ll have a definitely legitimate marking scheme.
- Otherwise, we’ll mark your solution
like how English teachers mark your essays (i.e., assign a random mark)roughly according to the following rules:- ~100% of the full marks for a complete and correct solution.
- ~85% of the full marks for a solution with a minor flaw.
- ~50% of the full marks for a solution with a major flaw.
- ~30% of the full marks for significant progress.
- ~15% of the full marks for minor progress.
- ~0% of the full marks for good jokes and memes.
- ~-15% of the full marks for bad jokes and memes.
- Therefore, even if you don’t solve a problem, still submit any interesting observations you noted–you may get part marks!
- \(b = 0\) if you didn’t cheat, and \(b\) satisfies \( (b^2 - 1)/(b - 1) = 2 \) if you did cheat.
- \(a\) (\(0 \leq a \leq \sum_{k=1}^{12} k \)) will be based on the mathematical rigor, completeness, and clarity of your solutions
- Awards:
- Overall Gold/Silver/Bronze (awarded to the top 3 teams)
- Overall Honorable Mentions (awarded to the teams ranked 4th to 6th)
- Division-based Gold/Silver/Bronze (awarded to the top 3 teams in each age division)
- Division-based Honorable Mentions (awarded to the teams ranked 4th to 6th in each age division)
- Prizes: None cuz we’re broke.