So I think that many people has seen this. So why do some people still have such a thought, that whenever a problem is seen, always try "All (some) of the variables are equal."? (Of course, guessing is acceptable, but typing out the solution that way is awkward!!!)

Just curious, so don't blame me please. And yup, I did do so, but only for guessing.

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I just want to let the numbers grow. Anyways, you are not the first one who asks me this XD

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People have different interpretations of what constitutes a "solution". Not everyone is trained in rigor / proofs.

In such a scenario, I love to link to inequalities with strange equality conditions.

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Excuse me, I don't really get it. Can you please explain further?

About the link, I did mention it in my note.

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People have different interpretations of what constitutes a "solution". They think that "Oh, because I tried these variables and got the numerical answer, hence I am correct". They are not aware of what a proof is, and why they need to (in this case) rigorously demonstrate that they have found an extrema, instead of just "I happened to enter the correct answer".

It is quite a common misconception that expressions achieve their extrema when all variables are equal. This is not true even if we restrict our attention to cyclic or even symmetric expressions. To further drive home this point, I link out to the wiki which has a lot of such examples.

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What is the problem called?

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"BAM k is max" it is.

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It's easier to just give the link here.

To answer your question, most people are not really interested in figuring out how to solve it, the education system has brought them up that way.

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To be honest, I'm very surprised. I've already heard of such education system (at least in my city) but typing the answers ONLY is not why Brilliant is made (I think). Besides, I don't think that an American (nope, I don't want to imply anything, seriously) will give such a solution. I mean their education system, in my opinion, is very improved. That raises me to this question.

Also, if only it was 2 or 3, that'd be great. But I think I've seen about 50 solutions (sorry, I mostly do Inequalities so I don't know much about other topics) with stuff like "Answer is... when..." and no clear explanation. If I could remember them, I'd have posted it here so you could see how awkward it is.

Anyways, can you please explain more about such system? I think I haven't known everything about that (all I know is that teachers fake their scores so they could promote, and students now just try to solve problems without understanding what they are doing).

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What is the link for brilliant lounge? Is it accessible through the brilliant website?

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