ComplexBash: The tool for Olympiads!

First of all, sorry for my long absentee, sorry to Brilliant.org and also to all who tried to contact me. I wasn't much active because of being a bit busy, but I think it had a good reason, and it's that now I can be more helpful to all...

This note is for all people who like solving problems from Math Olympiads, and many times find it difficult to notice the key property that solves a problem.

I want to start this thing about spreading bash, because when I started studying for Math Olympiads, books were really helpful, I even shared what I knew about them. It was books, that helped me reach till the IMO training camp of India.

But when I went to IMOTC 2015, I learnt a lot of things and one of them was

$\color{#3D99F6}{\text{The best help for something can be from someone who has done it before!}}$

I learnt a lot many things from seniors at the IMOTC 2015, and one of them was the use of Bash! It's a really very very useful tool for all who want to appear to Math Olympiads.

Bash :-

Bashing is solving a problem by methods which are not generally expected, for example solving a pure geometry problem by Coordinate geometry.
For bashing geometry, several known and widely used techniques are Coordinate geometry, Barycentric Coordinates, Complex numbers.
The reason why people do not generally motivate you to bash is because it just makes a problem, an actual problem that requires brain into just equations and calculations.

This means by bashing, we are just reducing the level of intelligence and knowledge required for solving the problem, and obviously nobody would promote that!

But guys, you know what? Even if people do not promote bash, they have to give full credit to a bash, $\text{if it is complete}$ ! Even in the Olympiads!

Coordinate geometry is a tool known to almost all people who appear for Olympiads, and it is a very useful tool. But sometimes it gets too tedious because of the many many equations and calculations.

But Complex numbers are actually coordinate geometry in a disguise, a disguise which is much shorter, sweeter!

The following comparison might highlight the importance of the use of complex numbers in Olympiad geometry.

img

If the table seems not readable, here is the original image

This note is part 1 of the bash-training I intend to start for Olympiads.

$\color{#3D99F6}{\text{There will be more, with examples of actual bashing,}}$ $\color{#624F41}{\text{based on the response to this note.}}$

This note is intended to be a conversation, so share your views.

If this topic interests you, I'll be posting examples and tricks in complex-bashing.

This not is inspired from Jorge Tipe's Peru MO training and I intend to help all the beginners who wish to do well... So share this with your friends.

$\color{#20A900}{\text{To the beginners - }}$ Make use of the notes for enhancing your skills and $\text{Bash all the problems!}$

$\color{#20A900}{\text{To the veterans - }}$ Help in this thing by sharing the new things you know!

Thank you for reading and there will be more coming!

Happy Problem Solving...

Interested in learning further?

Here's the Part 2 of this note

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paragraph 1

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[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"

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}

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

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

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}`	$\boxed{123}$

Comments

Algebraic bashing is a skill that China and South Korea train in. Singapore does that too, to a slight extent. There is definitely something comforting in knowing "Alright, at the worst, I can spend 2 hours on IMO problem 1/4 and get it out, if they are an inequality or a geometry problem".

There have been Olympiad problems where the official solution (before they looked at what contestants did) was through a bashing approach. Sometimes, they are even "magical" in the sense of "Oh look at this amazing algebraic identity that one would not normally think of".

Calvin Lin Staff - 5 years, 10 months ago

It's awesome. I appreciate that you shared it so that many others can learn. I am sure it's gonna help a lot of guys here on brilliant.org.

All the best! KEEP it Up. And thanks for sharing it. $\ddot \smile$

Sandeep Bhardwaj - 5 years, 10 months ago

Yeah well, you come in the type $\color{#20A900}{\text{To the veterans -}}$ so you'll be sharing your knowledge in this process, right? :)

Aditya Raut - 5 years, 10 months ago

Yup, right.

Nice note bro! Waiting for another.... :)

Harsh Shrivastava - 5 years, 10 months ago

Unfortunately, I used to bash Geometry problems in INMO using Co-ordinate! :( :'(

Satyajit Mohanty - 5 years, 10 months ago

Yeah right, I also used coordinate geometry in this year's INMO (was long long, but correct)... and then I learnt complex bash, which made things bit easier...

Well... that is great.. I'd love to learn new ways of solving the old problems. Your table made me to take Complex numbers more seriously than I usually did.

Rishabh Tripathi - 5 years, 10 months ago

Can I make questions in RMO using coordinate geometry ?

Sarthak Raj - 3 years, 11 months ago

no you can't because its rmo but its okay to use in inmo

Shivam Jadhav - 3 years, 11 months ago

Nice note! R u giving physics Olympiad???

Aditya Kumar - 5 years, 10 months ago

aditya bhai thanks. please post some questions also . and reply to the mail i have sent you a month ago.

Shivam Jadhav - 5 years, 10 months ago

Yeah sorry, that is why I've mentioned at the start of the note 'Sorry to all who tried to contact me' ...

thanks please post some questions to me

anisha mohapatra - 5 years, 3 months ago

Great work! Keep it up.

Deepak Kumar - 5 years, 10 months ago

Congrats on clearing the Olympiad !, Are you going to give Chemistry olympiad?

Rudy Raval - 5 years, 3 months ago

img links are ded :< , but thanks for these :-)

Arnav kumar Sinha - 4 months, 1 week 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}`	$\boxed{123}$