# 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?

Note by John Ashley Capellan
4 years, 8 months ago

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears 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} $$\boxed{123}$$

Sort by:

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).

- 4 years, 8 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.

- 4 years, 8 months ago