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https://math.stackexchange.com/questions/4094863/ Original title: Olympiad Geometry, How can I find values of c such that f(c) is even? I have gotten an equation of c !!

The OP was busy deleting the question while I was typing my comment:

I have also gotten an equation of c. They gave me antibiotic cream.

deleted by owner; someone left the page of the contest organzers: https://www.cemc.uwaterloo.ca/contests/dates.html

ORIGINAL: I have been noticing lots of questions that include the number 2021 as part of the statement. My impression has been that this makes it likely a contest question. Also, such questions NEVER include a source.

Today we have

Find all $ a,b,c \in \mathbb{R} $ that satisfies the equations, $ \bullet $ $ a+b+c=63$ and $ \bullet $ $ab+bc+ac=2021$?

Find $f(2021)$ if the function $f$ satisfies following conditions,(a)$f(1)=1 $, (b)$ f(x + y) = f(x) + f(y)$, (c) $f( \frac{1}{x})= \frac{f(x)}{x^2}$

enter image description here

So, rough estimates, what percentage questions with constant 2021 are important current contests (asking in April), how many are less crucial in some ways, how many are contests past submission deadline, .....

In particular, do people working up contest training problems use the year 2021 in such materials? How likely is it that one of our posts with the constant 2021 is training/prep?

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About the lack of source: one time I pushed really hard with an OP, saying that the "friend" who gave him the problem did not exist. He then pointed out that there really was a friend and that the question was university entrance. So, cheating in a different way from what I expected.

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    $\begingroup$ I think that a lot of homework turnover is done this way as well. I remember back when I was a student that many of the numbers involved were usually very close to that year. Especially when the questions were combinatorial or number theoretic where the solution is easy if you understand the formula (i.e. if you're writing the assignment for the students). $\endgroup$
    – Asaf Karagila Mod
    Apr 8 at 16:24
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    $\begingroup$ @AsafKaragila thanks. There is also a difference in style from homework questions to contest, the latter sometimes very tricky but requiring little knowledge... $\endgroup$
    – Will Jagy
    Apr 8 at 16:31
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    $\begingroup$ I was never good at contests, so I never really bothered to understand their "style". But I'm absolutely sure that you're right, since homework aim to test and practice something and contests aim to trick and confuse, to some extent. Maybe someone who's an expert in both can give their opinion. $\endgroup$
    – Asaf Karagila Mod
    Apr 8 at 16:37
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    $\begingroup$ Based on the question title, I presume that this is a question on Bayesian inference? Maybe try Cross Validated? :P $\endgroup$
    – Xander Henderson Mod
    Apr 8 at 16:47
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    $\begingroup$ More seriously, I suspect that most questions with [current year] involved as a constant are from some kind of setting in which timing is relevant (e.g. a competition, homework, exams, etc). Unfortunately, this is not really enough to go on vis-a-vis the competition policy. But it can be a signal that some Googling might find the source, or that answerers should maybe take a minute to think about whether or not they should answer the question before learning the source of the problem. $\endgroup$
    – Xander Henderson Mod
    Apr 8 at 16:49
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    $\begingroup$ @XanderHenderson right about Bayes, I did feel I had to restrict to questions with 2021 and ask conditional probabilities. As to timing being relevant and site policy, I can see that revising rules is not, well, frequent. I would feel a bit better if the kids would just take a moment to identify the source of a problem. $\endgroup$
    – Will Jagy
    Apr 8 at 16:55
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    $\begingroup$ I guess contest problems should be perfect, complete, unique, a little bit fascinating, right? I just couldn't understand what $f\left(\frac 1x\right)$ means in the first question. Since a real olympiad problem cannot be flawed, it seems to me that somebody made it up.. If not, then the intention is to deceive the contestant. But no prestigious contest problem can be in such a context. At least we can assume that this is a non-prestigious, maybe school-based competition question. $\endgroup$ Apr 8 at 19:32
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    $\begingroup$ Two such questions were asked by the OP in your first link, Will Jagy, and the OP deleted them both after first vandalizing them. I rolled back both to the their most recent, non-vandalized posts. $\endgroup$
    – amWhy
    Apr 8 at 23:10
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    $\begingroup$ Just wanna ask, but is there any way you could put the OP on "radar" for a while, as in having their questions checked by a mod before uploaded to ensure they are not contest questions, for the until the contest months have passed $\endgroup$ Apr 9 at 13:20
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    $\begingroup$ Must ... resist ... temptation ... to post ... a question: Is $x^{2021} + x + 1$ irreducible? $\endgroup$
    – hardmath
    Apr 10 at 23:09
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    $\begingroup$ @hardmath no, divisible by $x^2 + x+1$ because $2021 \equiv 2 \pmod 3$ $\endgroup$
    – Will Jagy
    Apr 10 at 23:11
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    $\begingroup$ @willjagy I'm curious now: is there a way to justify this without using complex numbers? The beauty of complex numbers is that it generalises well to similar polynomials: for example $x^n + x^2 + x + 1, n \equiv 3 \pmod 4$ is always irreducible, or $x^n + x^{k-1} + x^{k-2} + \cdots + 1, n \equiv k \pmod {k + 1}$ in general. $\endgroup$
    – Toby Mak
    Apr 11 at 11:56
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    $\begingroup$ Yes. Taken modulo $x^2 + x + 1$, $x^3 \equiv 1$. So, $x^{2021} \equiv x^2 \pmod{x^2 + x + 1}$. $\endgroup$ Apr 15 at 16:55
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Unfortunately, OP’s concerns are right about the first link. I have written the Euclid contest yesterday. Today, after looking at the title of the first link posted by the OP, I remembered the question immediately. After a quick check on the website, there are at least 3 more questions from the contest (I suspect there are more, but they might have been deleted by the posters).

Here are the links for the ones I could find:

I have not numbered the questions in accordance with the numbering in the contest.

To give some context, this exam is written by North/South American schools on the 7 th of April and is written by non-North/South American schools on the 8th of April. One purpose of this exam is to consider students for scholarships by the University of Waterloo, but most people I know only join for fun.

Individuals are allowed to write this exam remotely under “supervision” (but, to my understanding, supervisors can be anyone). The problems are not supposed to be discussed within 48 hours of the exam. What is worse is that these problems were posted during the contest hours.

We will have to wait for the contest problems to be released by CEMC.

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    $\begingroup$ thanks. That business of scholarships is one direction that worries me. If it would help to see deleted content, that can be arranged, a screenshot by a 10K user can be pasted here, the main requirement is that someone be able to find the thing. $\endgroup$
    – Will Jagy
    Apr 9 at 2:06
  • $\begingroup$ @WillJagy It would definitely help, but I don’t know if we can delete questions based on my memory. We should probably contact the university, but I think we are a bit too late since the contest should be over by now. $\endgroup$
    – dodoturkoz
    Apr 9 at 7:31
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    $\begingroup$ @Will Jagy Hi, Will. I have been "a victim" (an exaggerated term!) of this cheating, although I detected something abnormal that I noticed and wrote explicitly: this guy had previously posted the problem and, less that 5 minutes later, erased it, then reposted it 12 hours later. In a retrospective thought, I should have refrained from answering... $\endgroup$
    – Jean Marie
    Apr 9 at 8:14
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    $\begingroup$ @JeanMarie It will be a bit like a philosophical comment but, I have never seen any people succeed with such methods.. $\endgroup$ Apr 9 at 8:45
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    $\begingroup$ @lone student Said in a contraposive way, being honest is, at least on the long time, rewarded. $\endgroup$
    – Jean Marie
    Apr 9 at 8:48
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    $\begingroup$ @JeanMarie I checked your "victim" link; you are right, the guy is cheating. Also, we have all answered questions that might have been better ignored. It is a bit more clear if a question fits our own activities: this question from Sunday was interesting, while it was clear the OP did not have the background. I wrote up a Latex solution on my home computer and did email that to Keith Backman; math.stackexchange.com/questions/4088971/infinitely-many-primes Of my own wish list, I want to know the question source, and I don't like it when the OP does not know what the words mean $\endgroup$
    – Will Jagy
    Apr 9 at 14:29
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To answer the titular question:

The likelihood that a question with 2021 is from a current contest is $1-\dfrac1{2021}$.

Well, we all know that this likelihood was already quite high even before Math SE came around, and it only increases over time for questions on Math SE, since cheaters have found (empirically) that they can get away with a large fraction of their cheating episodes. So by now it ought to be close to $1$.

By the way, I used to be a regular participant in both mathematics and programming contests, so I do know very well what contest problems of both kinds look like. I want to add that programming contest problems in themselves almost always provide sample input and output, so just because you see an example does not imply that the asker has put in a single newton of effort.

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    $\begingroup$ Good points. Along with effort, I would like the source of the problem (not forthcoming if they are cheating) and assurance that they know what the words mean. For course homework, there can be some traction in both desiderata; for contests, not so much $\endgroup$
    – Will Jagy
    Apr 18 at 15:02
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    $\begingroup$ @WillJagy: Indeed. Supposedly, the current no-context close-reason is meant to indicate that context tells us why the asker is interested in the problem, which includes the source and any effort made and motivation for wanting to solve the problem to begin with (hopefully not because they want to cheat). Unfortunately, that close-reason is so softly worded (in my opinion) that few actually know that that is what is meant. $\endgroup$
    – user21820
    Apr 18 at 15:21

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