Do Brilliant problems require mostly ingenuity or a lot of knowledge?
Do most of the problems on brilliant require a lot of ingenuity or do you need to have quite a lot of knowledge on a wide number of topics for particular problems? People who are of high levels can you give me any advice on how I can improve and elaborate how you improved yourself. Thanks.
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Johnson Adeleke
8 years, 5 months ago
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In my experience it varies depending on the problem. Some of them have required extensive hard applications of things I have learned. I periodically find myself teaching myself or inventing for myself reasoning and math that I did not know before attempting the problem.
I think it does depend on the subject. Problems in geometry, number theory, and especially physics often require you know a certain theorem (geometry), technique (number theory), or equation (physics). For example, there've been a couple geometry problems where I've gotten stuck until I realized I didn't know a necessary theorem (I will admit, though, that most of the knowledge required in Brilliant problems isn't too complicated). On the other hand, I've been able to figure out most problems dealing with sets without ever having studied them formally.
One way I've been able to check what I need to improve on is by looking over problem solutions. If theorems are mentioned that I don't know, then I figure that I need to acquire some extra knowledge to succeed in solving those kinds of problems. On the other hand, if I have all the required knowledge but just wasn't able to put it together to arrive at the answer, then I figure that I need to work on problem solving skills. Idk if that makes sense, just a suggestion...
There is no set 'curriculum' that I follow. Most of the questions involve the student making some kind of 'insight step' which helps them to approach. [Of course, there are questions which test basic understanding of concepts too.] I try and keep the amount of knowledge required to a bare minimum, and pose questions which involve critical thinking. Most of the 'straightedge' Geometry questions are about applications of Sine Rule / Cosine rule, or trigonometric functions. I stayed away from Ceva and Menelaus thus far, even though they are really basic, because they are not 'naturally occurring' in a standard high school syllabus. However, vectors (and dot product) will be considered fair game, since that tends to be more extensively dealt with.
@Johnson The material isn't limited in scope. There are lots of concepts used which are not developed on the blog as yet. For example, there are questions on recurrence relations, but no mention of that on the blog. Some of these concepts will lend themselves naturally to blog posts, like the ongoing series on Permuations and Combinations.
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Well I dont agree with keeping vectors, beacuse being a ninth standard student, it is very difficult to me to first of all even understand the question, and the analysis and solution of the problem is literally impossible. I think usage of Ceva's and Menalaus Theorem in questions is generally seen in the olympiads.
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being a student of class 9 i completely agree with shourya..........pappus theorem , menelaus theorem,cevas therom should be introduced..........vector is good,i.e not bad,,,but not totally fair as we have vector in class 11 or 12.........i can do the basics but not the ultimatum
@Johnson. I am not the greatest problem solver in the world or on this site. But I think variety of problem style and type really helps my problem solving skills.
generally speaking, i think they do require a decent amount of knowledge but at the same time, some ingenuity in applying it to these problems
Yeah, I agree with Anas a bit but it tends not to work most of the time so i go the blog which is really helpful. Calvin, are all the notes on the blog used in creating the problems we get and only the material that the blog has ? If not do you have any advice on good books or websites that I could got to :).
Oh I see so basically I should just improve my mathematical problem solving skills? But how and with what?
The most important thing is practise. Intelligence does help, but many of the problems which are tackled in the Olympiads require practise. People practise a lot. You should appreciate their hard work. I know some people who have performed very very well in the olympiads and they say it's practise, practise and intelligence to some extent. As Jacob P comments above, its the variety of problem solving that really helps. Getting familiar with the problem solving techniques is what matters most.
Well I think both are required. Small questions are generally more theoretical, but the more marks questions might need an interesting approach.
I'm interested in knowing what others think too!
Hi, for me, I check the problem's name, then I google for it, it helps me have a general idea about it. wikipedia often gives theoremes with a relation to it. if I'm despite of that, I didn't succeed, then I google for the terms, (key terms),like monic polymonials, equationnal funtion solving, or something like that.
For the problems in my level, I feel that the math problems don't need too much knowledge (maybe just a bit out of the high school curriculum). A lot of them still require a lot of thinking, even if you know what mathematical tools you need. For physics, some of the questions just require knowing the formula and plugging numbers in, but there are also much more nontrivial problems in which knowing what's going on is the majority of the battle. The math to calculate the answer is simple in comparison.