Finding Hard

I recently found out that in Brilliant, I found the area of Combinatorics hard because I always go to Level 3, then go back to Level 2 again, and go back to Level 3 again... Cycle goes again and again. Are problems in Combinatorics really hard to solve? What advice can you give me to achieve higher? What might be a good combinatorics reference?

#Combinatorics #Advice

Easy Math Editor

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`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}`	$\boxed{123}$

Comments

Go study the combinatorics section here on Brilliant (https://brilliant.org/assessment/techniques-trainer/#olympiad). That should give you the tools to get up to level 4. Unfortunately, by then the problems start being less about pure combinatorics and more about combinatorics applied to other areas of mathematics. For instance, in my brief time at level 5, one of the problems I faced required reasoning about 8-dimensional space, which I completely lack the background to do. Another was apparently intended to be approached more as a logic problem than a combinatorics one. Last week a problem in level 4 involved reasoning about rational vs. irrational numbers. Several have relied on knowledge of number theory.

As far as hardness, it seems to be easier to make subtle mistakes with combinatorics (forgetting to count certain cases, or double-counting other cases).

Christopher Johnson - 7 years, 7 months ago

ITYM the 7-dimensional space question? Yeah, that was horrible. It was hard because 7-d was a special case that worked, and there was no solution for 4,5,6 dimensions.

Matt McNabb - 7 years, 7 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}`	$\boxed{123}$