# What kind of context is good to add to a contest math question?

This is a call for brainstorming for ideas on how to best make questions from math contests meet our quality requirements, outlined in many places, but How to ask a good question is the most commonly used reference. I am particularly interested in what type of context could/should be added to a contest question.

The goal is to help

• the asker (= OP), who may be a new user, as well as
• a curator = anyone who wants to save a question they like from attracting negative attention.

Of course, some of you may think that adding context to any question is unnecessary, but I am assuming that the policy will stay in something close to the presently enforced form, and want to cater for that.

Why I think contest math questions require extra pieces of advice?

You may think that contest questions don't need any special treatment, after all the rule should be the same for all questions. That's fine, of course. If we get good material here, you may still want to peruse them.

I think the policy on PSQs is mostly targetting homework questions. At least it's safe to say that homework questions form the largest group of material failing to make the grade. The tips

• avoid "no clue" questions,
• where the question comes from

are commonly used. But these are, in my opinion, a bit problematic when applied to contest questions. Let me elaborate:

• Even a relatively talented asker may be truly clueless when facing a well designed contest question. This is because that is often exactly the goal of whoever designed the question! This is in sharp contrast to homework assignments.
• For the same reason it may be impossible for the asker to show their own efforts. The first hurdle of getting anything done with a contest question is often the highest.
• A contest question absolutely should identify itself as such, including its source, if only to comply with our policy on questions from on-going contests. But otherwise it may be difficult to explain "where the question comes from" in the sense that a contest question does not always come with a clearly defined topic or tag – unlike a homework question from a given chapter of some textbook.

I'm feeling lucky today

If we get enough good material here, I will just link this thread to the How to ask thread. If we get too much material, I guess I need to volunteer to compile a summary, and add it as an answer there :-)

• See also this old related thread discussing the differences and similarities of homework vs. contest questions. – Jyrki Lahtonen Jul 23 at 18:11
• Do we really have any extra advice(s) specifically for contest type questions? The examples you provided in the answer below seem to work with all (not so trivial) questions. – Arctic Char Jul 23 at 18:34
• @ArcticChar I do think it makes sense; there are specific aspects. I repost what I just mentioned on the answer. (1) The fact that it is a contest question (2) Which contest exactly, what is the nature of the contest. (3) Why does the questionneer ask. // I think at the very least 1 and 2 ought to be non-controversial. – quid Jul 23 at 18:38
• I am not sure @ArcticChar. I still hope to collect material. This thread was created partly to help users like Batominovski, who was desperately trying to salvage a contest question. One of the cases leading to this discussion. Mostly this is because I have some affinity with contest questions, and am somewhat miffed by them getting treated just like homework questions. An admittedly fond hope is that contest question askers could apply some suggestions a typical homework help seeker cannot. – Jyrki Lahtonen Jul 23 at 18:40
• Sorry. In part what I said is mentioned in the post. But it is not explicitly mentioned as a requirement. – quid Jul 23 at 18:42
• @quid A list of required context (= yours) should definitely be given as an advice. I will add it, at least to the "final" version. – Jyrki Lahtonen Jul 23 at 18:44
• How do we define contest questions exactly? Do they really have to come from contests? I count all practice problems (or problems that look like they are geared towards contests) as contest questions. These practice problems often times do not come from any contest. – Batominovski Jul 23 at 18:52
• @Batominovski I would tag questions from contest training as contest-math. I don't know if this is a common policy. – Jyrki Lahtonen Jul 23 at 18:56
• One might briefly explain why the question is difficult, like this one – Arctic Char Jul 23 at 18:56
• @quid I don't wanna see questions like: "The following question is from [name the contest, name the year]. Question "...........................................". "I don't know how to solve it. Please help me." wannabe contest participants don't learn much from reading others' solutions, without effort on their part, to start. – amWhy Jul 23 at 19:05
• @amWhy That is also a valid concern. Some such askers are clearly out of their depth, and should try their hand with simpler training problems first. They may have started contest training with unrealistic expectations, or simply be misinformed of what contests are about. "Can you recommend a book that would explain this?" makes me squirm. – Jyrki Lahtonen Jul 23 at 19:11
• @amWhy I did not mean my list to be necessarily comprehensive. That said what you said is still relatively better than the question without that information. I meant to say at the very least that information must be given, and this should be uncontroversial at least for 1 and 2. – quid Jul 23 at 19:15
• I agree, @quid. What you listed were necessary conditions, but not necessarily sufficient? – amWhy Jul 23 at 19:20
• @amWhy yes that was my intent. – quid Jul 23 at 19:44
• Usually the students who participate in such contests go through some comprehensive training / preparations (either via books or some tutoring) and in general not as clueless about such questions as a typical student. But yes there may be really tricky problems where one can't expect any attempts, but certainly a sincere asker interested in solution may share some thoughts about the problem rather than just mentioning name and year of contest along with problem statement. – Paramanand Singh Jul 27 at 11:12

One way for the asker to show effort on a taxing contest question is to

Work out a simple(r) case

This is also good advice towards solving the question (straight out of Polya's How to solve it).

• A question often has a parameter, and sometimes checking what happens when the parameter has a fixed (smallish) value will be much easier than the general case.
• Such effort works as experimentation (which is why it is in Polya's book), possibly leading to a solution eventually.
• The parameter may be hidden. A popular fad is to include the year of the contest as the value of a constant appearing in the problem. Sometimes this is a red herring, and replacing $$2020$$ with $$3$$ will already reveal something interesting. Often such testing won't reveal much as the underlying problem design may simply require that parameter to satisfy an unknown congruence (to be revealed). On other occasions the exact value is not important but it has to be large enough to allow a pigeonhole argument to work. Anyway, replacing that constant with a more manageable one is often the way to go.
• A problem in geometry may have easier simpler cases, if you assume some extra symmetry condition.
• An inequality is often trivial, when the free variables are all equal (that is surprisingly often also the extremal case).

The last two bullet points may be overdone, and not convince a reviewer of a serious effort, but if that's all you can show it beats having nothing at all.

These suggestion may also guide a homework help seeker, depending.

• Would you count saying something about the equality cases in an inequality question as a good context, however trivial the equality cases may be? In most cases, it doesn't require too much effort. – Batominovski Jul 23 at 18:45
• I also am very sympathetic towards geometry and combinatorics problems. I have been totally stumped with these questions, without any insight what to do. Combinatorics questions sometimes offer no simplifications. For geometry problems, sometimes you can at least draw some lines, but I'm not sure that saying "I have drawn these lines/circles and got nowhere" is an acceptable context for most critics. – Batominovski Jul 23 at 18:45
• @Batominovski That is exactly the concern that lead me to adding the next sentence. Oversimplification is not very convincing as effort. – Jyrki Lahtonen Jul 23 at 18:46
• It is often the case that there is an apparent, if inelegant, mode of attack and a thoughtful sentence or two describing such a method (perhaps including an indication as to why it is computationally unwieldy or the like) would go a long way. – lulu Jul 23 at 18:48
• Something similar to this advice on attempting easier cases is already a part of the guide on how to ask good questions - specifically, advice like picking special cases or smaller numbers is mentioned in the avoid "no clue" questions post. While this information is useful, I'm not really sure it advances the discussion much. – KReiser Jul 23 at 22:42
• I agree with @KReiser. I don't think questions tagged "contest math" deserve any special treatment already addressed in the post "How to ask a good question". That contest questions need to include the year/date and contest name is an added requirement. But making a special set of criteria for contest questions, as opposed to questions in general, isn't necessarily helpful. I don't want to have to refer to two or three or five, or eight posts to recommend to users how to ask a good question, across the board. – amWhy Jul 24 at 1:16
• Point taken @amWhy :-) That's why my default plan is to add the fruits of this thread to that "master guide". Either edit a link leading here into WW's question or post a summary. Let's see how this plays out. – Jyrki Lahtonen Jul 24 at 16:13
• Agreed @KReiser. So far it doesn't look very good. I may elaborate on this later. My preconceived impression was that people in contest training are generally more capable of following certain kinds of suggestions in comparison to a typical homework help seeker. This impression may say more about me than about the asker :-) – Jyrki Lahtonen Jul 24 at 16:16
• Jyrki, there are a million "My friend told me this problem," see math.stackexchange.com/questions/3764736/… – Will Jagy Jul 24 at 16:28
• @WillJagy LOL. That always reminds me of the story. A dude visits a doctor and starts talking - A friend of mine suspects that they have caught a VD. How can he tell for sure? The doctor replies - Just whip out the "friend" and we'll take a look. – Jyrki Lahtonen Jul 24 at 16:33

There are variations when the person posting the question is lying. People are aware of ongoing contests. This is one reason I ask for a source of the problem. At least once, some kid posted a problem from a long list of proposed questions, one that was not chosen since the desired conclusion was wrong. There are ongoing programming contests.

About lying, once I pressed repeatedly when a guy claimed his friend gave him the question. I kept saying there was no friend. In the end, it turned out there was a friend, and this was a question from one of the university entrance exams they have in India and some other countries. So, there was a friend, but this was still illegitimate. Meanwhile, if there really is a friend who got the problem from some organized contest preparation, this does not imply that the person posting knows anything about the context of that contest prep. See Solving for positive reals: $abcd=1$, $a+b+c+d=28$, $ac+bc+cd+da+ac+bd=82/3$

Let's see, I prefer if the OP knows what the words mean.

• I fixed a typo. I was confused for a little while what "his friend gave hi the question" meant. How do you give hi something? – Batominovski Jul 24 at 16:13
• @Batominovski modern slang, you just never know. I saw you also corrected a parenthesis on the $a+b+c+d=28$ question. My opinion is still that the realistic way to reduce to non-calculus inequalities is to write it out in a different basis, $(a,b,c,d)$ is $$w(1,1,1,1) +x(-1,1,0,0)+y(-1,-1,2,0) + z(-1,-1,-1,3)$$ If desired, not clear whether important, the vectors can be normalized to length $1$ first. – Will Jagy Jul 24 at 16:18
• I've been wary of competition problems since I was seriously burned by a poster lying about the source: question link. Turns out "tough question taken from a quite easy maths puzzle book" was code for "active competition." By the time it was discovered, it was too late, and the poster would have been mathematically competent enough to avoid just copying the answer. Left an awful taste. – Peter Woolfitt Jul 25 at 4:11
• @PeterWoolfitt yes. The question I linked, supposedly it comes from contest preparation for a middle-school student. That is just not a realistic description. No guarantee it is in an active competition either; just that it was interesting enough that I got caught. – Will Jagy Jul 25 at 15:47