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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

\(\color{Blue}{\text{The best help for something can be from someone who has done it before!}}\)

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.



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.

\(\color{Blue}{\text{There will be more, with examples of actual bashing,}}\) \(\color{Brown}{\text{based on the response to this note.}}\)

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.

\(\color{Green}{\text{To the beginners - }}\) Make use of the notes for enhancing your skills and \(\text{Bash all the problems!}\)

\(\color{Green}{\text{To the veterans - }}\) 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

Note by Aditya Raut
1 year, 3 months ago

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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 · 1 year, 3 months ago

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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 · 1 year, 3 months ago

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@Sandeep Bhardwaj Yeah well, you come in the type \(\color{Green}{\text{To the veterans -}}\) so you'll be sharing your knowledge in this process, right? :) Aditya Raut · 1 year, 3 months ago

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@Aditya Raut Yup, right. Sandeep Bhardwaj · 1 year, 3 months ago

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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 · 1 year, 3 months ago

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thanks please post some questions to me Anisha Mohapatra · 7 months, 3 weeks ago

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Unfortunately, I used to bash Geometry problems in INMO using Co-ordinate! :( :'( Satyajit Mohanty · 1 year, 3 months ago

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@Satyajit Mohanty 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... Aditya Raut · 1 year, 3 months ago

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aditya bhai thanks. please post some questions also . and reply to the mail i have sent you a month ago. Shivam Jadhav · 1 year, 3 months ago

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@Shivam Jadhav Yeah sorry, that is why I've mentioned at the start of the note 'Sorry to all who tried to contact me' ... Aditya Raut · 1 year, 3 months ago

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Nice note bro! Waiting for another.... :) Harsh Shrivastava · 1 year, 3 months ago

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Nice note! R u giving physics Olympiad??? Aditya Kumar · 1 year, 3 months ago

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Congrats on clearing the Olympiad !, Are you going to give Chemistry olympiad? Rudy Raval · 7 months, 3 weeks ago

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Great work! Keep it up. Deepak Kumar · 1 year, 3 months ago

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