### Post log

This is the post log. The main motivation to make such a page was to help you use this blog in the best possible way!

The archive widget and categories could possibly help, but this page might suit your needs better. There is a basic preview for each blog post too!

This is constantly updated.

[1] How to start with Math Olympiad: This post starts with giving an unofficial guide to AoPS and then goes on to discuss various queries newcomers ask. Following up with some general tips.

This post, in short, discusses various methods to organise a solution and present it in neat ways.

[3] Q&A with experts about bashing: A post where various IMOTCers share their opinion on bashing Geometry problems.

[4]  Algorithms, or Mathematics? A post where we discuss "mathematical miseducation". We discover the true essence of Mathematics.

[5]A phase I'll never forget In this post, Pranav describes his experience organizing Unofficial IMOTC 2022.

Math

[1] EGMO Solutions, motivation and review: In this post, Atul, Pranjal and Abhay ( who are part of the OMC team) discuss European Girls Mathematical Olympiad 2022 Solutions with motivation and reviews.

[2] Basic Combinatorial Ideas Part 1: In this post, we see cute combinatorial ideas through different contest problems. We discussed ISL 2009 C1 (a), USAMO 1997 P1, IMO 2011 P4, USAMO 2002 P1, (adapted from) Canada 2018 P3.

[3] Construction in NT In this post, we discuss various theories around construction in NT along with problems.

[4] ISI Objective 2022 Solutions We discuss solutions for the ISI entrance exam 2022 with motivation.

[5] Linear Algebra in Graph Theory Here we will talk about two interesting applications of Linear Algebra in Graph Theory. It is highly recommended that you have some familiarity with Linear Algebra, such as the definition of linear independence, rank, rank-nullity theorem, determinants, and some idea of eigenvalues.

[6] The Art of Double Counting In this post, we will dive into the topic of double counting by working through some problems and hopefully be able to showcase how to employ the technique when the need arises for the same.

[7] Including and Excluding A post that will discuss some important ideas related to the topic.

[8] Combinatorial Games and Process In this blog post, We are gonna walk through some nice and instructive problems involving combinatorial processes and games that the author personally really liked.

[9]Minkowski's convex body theorem This blog post was based on Akshat Pandey's Sophie WeMP( Weekly Math Presentation).

This blog post was based on Malay Mahajan's Sophie WeMP( Weekly Math Presentation).

n this post we will talk about rational cubic curves.

[12] Logs and Bits This blog can be divided into two parts: In the first part, we would be talking about some basic but useful $log n$-ish algorithms, and later we would be discussing some construction-based problems whose solution exploits the binary representation of numbers. Both parts can be read independently too.

[13] Introduction to Recurrence Relations An introductory post to recurrence relations.

[14] Challenge the Rules A fun combinatorial game post where we challenge the rules!

[15] Dynamic Programming Dynamic Programming is one of the most popular techniques in competitive programming and a powerful algorithm design technique. This post is an introductory post to Dynamic Programming.

[16] Probability is Global An introductory post to Probability and expected value.

[17] LTE lemma This post discussed LTE and it's proof. LTE stands for lifting the exponent lemma.

[18] Mobius Inversion In this post, we talk about Mobius Inversion.

[19] Trust Issues A fun number theory post where we discuss ISL 2019 N5.

[20] Whose Game? In this blog post, we will talk about Combinatorial games, how to quantify positions, and analyse games. Most of this is based on the beginning chapters of the comprehensive book Winning Ways for your Mathematical Plays by Berlekamp, Conway and Guy.

[21] Top 10 problems We discuss the top 10 problems from Number Theory and Algebra.

### Constructions in Number Theory

Hi, I am Emon, a ninth grader, an olympiad aspirant, hailing from Kolkata. I love to do olympiad maths and do some competitive programming in my leisure hours, though I take it seriously. I had written INOI this year. Today, I would be giving you a few ideas on how to Construct in Number Theory . Well, so we shall start from the basics and shall try to dig deeper into it with the help of some important and well-known theorems and perhaps, some fancy ones as well. Okay, so without further delay, let's start off... What do we mean by "Constructions"? If noticed, you can see that you often face with some problems in olympiad saying, "... Prove that there exists infinitely many numbers satisfying the given conditions" or "... Prove that there exists a number satisfying the above conditions." These are usually the construction-problems .  For example, let's consider a trivial example : Problem. Prove that there exist infinitely many integers $a$ such th

### EGMO solutions, motivations and reviews ft. Atul, Pranjal and Abhay

The  European Girls' Mathematical Olympiad a.k.a EGMO 2022 just ended. Congrats to Jessica Wan from USA, Taisiia Korotchenko, and Galiia Sharafetdinova for the perfect scores! Moreover, the Indian girls brought home 4 bronze medals! By far, this is the best result the EGMO India Team has ever achieved! To celebrate the brilliant result, here's a compilation of EGMO 2022 solutions and motivations written by my and everyone's favorite IMOTCer Atul ! And along with that, we also have reviews of each problem written by everyone's favorite senior, Pranjal !  These solutions were actually found by Atul, Pranjal,  and Abhay  during the 3-hour live solve. In the live solve, they solved all the 6 problems in 3 hours 😍!!! Okie Dokie, I think we should get started with the problems! Enjoy! Problem 1:  Let $ABC$ be an acute-angled triangle in which $BC<AB$ and $BC<CA$. Let point $P$ lie on segment $AB$ and point $Q$ lie on segment $AC$ such that $P \neq B$, $Q \neq C$ and

### Q&A with experts about bashing

Heyy everyone! From the title, you can see that we are going to talk about  BASH.  Yesss, we are going to discuss whether you really need to learn bash or not?  Let me first introduce myself, I am Pranav Choudhary, a 10th grader from Haryana(India). I like to do geo and combo the most :PP. Oki so let's begin! For those of you who don't know what bashing is, lemme give you a brief introduction first. Bashing is basically a technique used to solve Geometry Problems. In general, when you try a geo problem you might think of angles, similarities, and some other techniques (e.g. Inversion, spiral similarity etc). All of which are called synthetic geometry. But sometimes people use various other techniques called "bash" to solve the same problems.  Now there are different kinds of bashing techniques, e.g. - Coordinate bash, Trig Bash, Complex bash, Barycentric Coordinates. Let me give you a brief introduction to each of them.  Coordinate Bash : You set one point as the orig