Combinatorics - Searching for Help

Hello there fellow mathletes! I just need some feedback on this topic.

Alright so when it comes to combinatorics, I am downright terrible. By that, I mean that I end up doing almost every problem just with logic and reasoning, which usually takes a very long time and is very prone to error. Whenever I check the solutions, I always see many people solving the problems with quick and nifty techniques like properly applying a binomial coefficient to solve the problem, or using some fancy technique to solve a probability problem.

My question is, how do/would you go about getting better at combinatorics? Would you just keep going at those problems?

Thank you very much!

#Combinatorics #Help

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
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`\frac{2}{3}`	$\frac{2}{3}$
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`\sum_{i=1}^3`	$\sum_{i=1}^3$
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Comments

My personal opinion is to keep on going with the problems, but take them very slow and deliberately. With persistence you do develop a better understanding of the nifty tricks which goes a long way in being able to recognize when they are useful in problems where it is not obvious(often the norm on Brilliant).

That said the valuable part of going after problem after problem is floundering at them within the limits of your own knowledge and creativity. When I flounder at math on Brilliant I rely liberally on pencil/paper, crude pictures that even my mother couldn't love, my fingers/toes, and the Techniques section. Scroll down to combinatorics. It is full of gems. I have little innate intuition for combinatorics and have reread and forgotten this post many times.

Peter Taylor Staff - 7 years, 5 months ago

Sometimes on harder combo problems (and problems in general actually) it may be helpful to try smaller cases and experiment. Try to explain your conjectures even if you got the right answer, it'll help you understand the problem better.

bob smith - 7 years, 5 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$