Post log

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

The archive widget and categories could possibly help, but this page is quite systematic. Moreover, I have given a basic preview of the blog post too!

This is always getting updated.

Total Posts: 47
Total problems discussed: 325

Miscellaneous Problem Discussions :

Top 10 problems of Week#1 I started a 4-week series, where I posted 10 problems each week, which had walkthroughs too.
Top 10 problems of Week#2
Top 10 problem of Week#3
Top 10 problems of Week#4
Week#5 This week, I posted two olympiad problems.
Geometry( Finally!!!) This was my first post that had Olympiad geometry in it! It had $13.$
High RMO level problems A collection of some nice diophantine which were overkilled by fancy NT theorems. It had $7.$
A Cute problem solution of a very cute Number theory problem I did. $1$ problem discussed..
Getting high with Geometry A collection of geometry problems with solutions from a few renowned books. $10$
Non-Geos are cool Started a series called Non-Geos are cool! The main motive is to get some cute non-geos that do not require that harsh theory! And is suitable for INMO level (Indian National Mathematical Olympiad). Featuring $5$ problems.
Non-geos are cool part 2 The second post of this series. Featuring $5$ problems.

Problems done in July Basically, at the end of each month, I will be sending the $5$ best problems I did in that month with the solutions. It might look a bit less to you, but I try to send $5$ problems each week. Doing the math, I will be sending $20$ problems in each month. With a level, probably equivalent to INMO (Indian National Mathematical Olympiad) or a bit higher.
Problems done in August Featuring some very cool Geos and cute polynomials! Featuring $10$ problems!
Geos are definitely cool Started a series called Geos are definitely cool! The main motive is to do some of the ISL geometries. And the series will increase in difficulty after each post! Collection $10$ ISLs.
Let's do problems only A pretty nice set of $20$ problems which are just INMO level.
Geos are my life support A set of $10$ nice geo problems explaining why geos are the best.
Number theory is my bias wrecker.html A set of nice $14$ IOQM- RMO level NTs
INMO problems $20$ past year INMOs which I did.
Birthday FEs I tried $11$ FEs
Number Theory revise part 1 I started a new series where I will revise the NT I learnt. This post has $13$ problems.
Number Theory revise part 2 Continuing with the above post, a collection of $11$ problems.
Number Theory revise part 3 Proved LTE and did $2$ problems..
Solving Random Problems before INMO Solved $9$ ISLs and shared $6$ sharygin.
Announcing the Unofficial TC A post where I discuss $13$ new problems of INMO~or INMO+ level!

Notes/Problem Sets :

Symmetric Polynomials I wrote notes for Symmetric polynomials.
Newton Sums (Sym Poly part 2) This was the continuation of the Symmetric Polynomials post and talked about Newton sums.
My first own problem set This was my first problem set. All the problems are my own, though ideas are probably not new. The problems are of the level AMC-8 or AMC-10 level.
School notes and more problem sets The post where I sent more notes( handwritten). And some more problem sets compilation.
Vectors The basic introduction to vectors. It covers all the fundamentals!
Let's complex bash part 1 A series where I am posting my notes to "Complex number in geometry."
Let's complex bash part 2 The second post of the series.
Probability is global Olympiad Notes on probability with $17+18=35$ problems.
Expected value Continuing from "the probability is global", we do expected value along with $16$ problems.
Recurrence Relations Olympiad Notes on Recurrence Relations where almost each problem is s different topic and makes us learn something new.
We have $14$ problems to solve.
Graph theory part 1 Olympiad notes on Graph theory. In this post, I talk about Degrees, degrees sequence, etc with $8$ problems and many theorems.
Graph Theory part 2 Olympiad notes on Graph theory. In this post, I talk about the Euler path, Ore's Theorem, Hamiltonian, etc with $8$ problems and many theorems.
Graph Theory part 3 Olympiad notes on Graph theory. In this post, I talk about planar graphs with $6$ problems and theorems.
Graph Theory Part 4 Olympiad notes on Graph theory. In this post, I talk about Independent sets and covering sets

Non-math :

Summary of 2020 A new year post and summary of 2020.
IOQM results and predicted INMO I talked about my IOQM and predicted INMO paper.
Cute cats part 1 One of the most loved series of all time. It's really fun compiling some cute cat pics and adding some relatable yet fun captions.
Cute cats part 2 This was very special since I wrote it for 5k views special.
Our cute Siblings Post is dedicated to all the elder siblings who have to go through this painful period :(.
Reflecting on past Post where I explore what stuffs went wrong ( and also had discussion related to INMO)

My experiences at EGMO, IMOTC and PROMYS experience

Yes, I know. This post should have been posted like 2 months ago. Okay okay, sorry. But yeah, I was just waiting for everything to be over and I was lazy. ( sorry ) You know, the transitioning period from high school to college is very weird. I will join CMI( Chennai Mathematical Institue) for bsc maths and cs degree. And I am very scared. Like very very scared. No, not about making new friends and all. I don't care about that part because I know a decent amount of CMI people already. What I am scared of is whether I will be able to handle the coursework and get good grades T_T Anyways, here's my EGMO PDC, EGMO, IMOTC and PROMYS experience. Yes, a lot of stuff. My EGMO experience is a lot and I wrote a lot of details, IMOTC and PROMYS is just a few paras. Oh to those, who don't know me or are reading for the first time. I am Sunaina Pati. I was IND2 at EGMO 2023 which was held in Slovenia. I was also invited to the IMOTC or International Mathematical Olympiad Training Cam...

Introduction

Hey Everyone!! This is my first Blog post. So let me give a brief introduction about myself. I am Sunaina Pati. I love solving Olympiad math problems, learning crazy astronomical facts , playing hanabi and anti-chess, listening to Kpop , love making diagrams in Geogebra and teaching other people maths 😊 . I love geometry , number theory and Combinatorics . I am starting this blog to keep myself a bit motivated in doing studies 😎 . Right now, I am planning to write walkthroughs on some of the best problems I tried over the week which can refer for hints 'cause solutions contain some major spoilers and one learns a lot while solving the problem on his own rather than seeing solutions . Also, there will be some reviews about Kpop songs, study techniques, my day to day lifestyles,exam reviews and ofc some non-sense surprises 😂. I am planning to try posting every week on Sundays or Saturdays ( most probably) ! Though there is no guarantee about when I ...

How to prepare for RMO?

"Let's wait for this exam to get over".. *Proceeds to wait for 2 whole fricking years! I always wanted to write a book recommendation list, because I have been asked so many times! But then I was always like "Let's wait for this exam to get over" and so on. Why? You see it's pretty embarrassing to write a "How to prepare for RMO/INMO" post and then proceed to "fail" i.e not qualifying. Okay okay, you might be thinking, "Sunaina you qualified like in 10th grade itself, you will obviously qualify in 11th and 12th grade." No. It's not that easy. Plus you are talking to a very underconfident girl. I have always underestimated myself. And I think that's the worst thing one can do itself. Am I confident about myself now? Definitely not but I am learning not to self-depreciate myself little by little. Okay, I shall write more about it in the next post describing my experience in 3 different camps and 1 program. So, I got...

INMO Scores and Results

Heya! INMO Results are out! Well, I am now a 3 times IMOTCer :D. Very excited to meet every one of you! My INMO score was exactly 26 with a distribution of 17|0|0|0|0|9, which was a fair grading cause after problem 1, I tried problem 6 next. I was hoping for some partials in problem 4 but didn't get any. I am so so so excited to meet everyone! Can't believe my olympiad journey is going to end soon.. I thought to continue the improvement table I made last year! ( I would still have to add my EGMO performance and also IMO TST performance too) 2018-2019[ grade 8]: Cleared PRMO, Cleared RMO[ State rank 4], Wrote INMO 2019-2020[ grade 9]: Cleared PRMO, Cleared RMO[ State topper], Wrote INMO ( but flopped it) 2020-2021[grade 10]: Cleared IOQM, Cleared INMO [ Through Girl's Quota] 2021-2022[grade 11]: Wrote EGMO 2022 TST[ Rank 8], Qualified for IOQM part B directly, Cleared IOQM-B ( i.e INMO) [Through general quota], 2022-2023 [grade 12]: Wrote E...

Geometry ( Finally!!!)

This is just such an unfair blog. Like if one goes through this blog, one can notice how dominated Algebra is!! Like 6 out of 9 blog post is Algebra dominated -_- Where as I am not a fan of Algebra, compared to other genres of Olympiad Math(as of now). And this was just injustice for Synthetic Geo. So this time , go geo!!!!!!!!!!! These problems are randomly from A Beautiful Journey through Olympiad Geometry. Also perhaps I will post geo after March, because I am studying combi. Problem: Let $ABC$ be an acute triangle where $\angle BAC = 60^{\circ}$. Prove that if the Euler’s line of $\triangle ABC$ intersects $AB$ and $AC$ at $D$ and $E$, respectively, then $\triangle ADE$ is equilateral. Solution: Since $\angle A=60^{\circ}$ , we get $AH=2R\cos A=R=AO$. So $\angle EHA=\angle DOA.$ Also it's well known that $H$ and $O $ isogonal conjugates.$\angle OAD =\angle EAH.$ By $ASA$ congruence, we get $AE=AD.$ Hence $\triangle ADE$ is equilateral....

Reflecting on past

INMO Scores are out!! I am now a two times INMO awardee :) I got 16|0|1, so 17 in total! Yes, 16 in P1 T_T. I was thinking I would lose marks because of the way I wrote. Lemme tell ya'll what happened that day but first I should share a few thoughts I had before the exam. My thoughts Honestly, my preparation for INMO was bad. In fact, I should say I didn't work hard at all. As I have said earlier, I had lost all my hopes for INMO and Olympiads as a whole after EGMO TSTs happened. Art by Jelena Janic EGMO TSTs i.e European Girl's Mathematical Olympiad Team selection Tests 2022. Literally my thoughts after EGMO TSTs I feel very ashamed to share but I got 1 mark in my EGMO TSTs. Tests in which I literally gave my whole life. I did so many ISLs ( like SO MANY), I mocked EGMO 2021 TST where my score was 28/42 and I perfected Day 2. 1 mark in the TST just showed my true potential. There are way better people than me in olys. A friend even said to me, "If I wouldn't...

Bio is Love..

Adios, everyone! Boards preparation at its peak :( However, I am not able to study how I used to. Every time I try to study for boards, I just keep thinking much about a topic, stare at the book, jam a song or just start doing procrastination by bookmarking random cute problems in HSO. It's been more than a year I have studied like with a focus on a book. My lappy is being a big distraction tbh. So after INMO score come out, I will just give my lappy for repair and say papa to bring it back home after June 2. Milk and Mocha I literally am taking 2 days to complete 1 bio chapter, some times even 3. The rate of my "slowness" is probably because I am like every 15 minutes checking discord to see if the INMO scores are out or not. So HBCSE, thank you for keeping me anxious. Funfact:- we must be grateful that there is an organisation that is conducting these national Olys. There are some countries where no Olys are being conducted. ( Same dialogue which mumma uses, but in p...

Solving Random ISLs And Sharygin Solutions! And INMO happened!!

Some of the ISLs I did before INMO :P [2005 G3]: Let $ABCD$ be a parallelogram. A variable line $g$ through the vertex $A$ intersects the rays $BC$ and $DC$ at the points $X$ and $Y$, respectively. Let $K$ and $L$ be the $A$-excenters of the triangles $ABX$ and $ADY$. Show that the angle $\measuredangle KCL$ is independent of the line $g$ Solution: Note that $$\Delta LDK \sim \Delta XBK$$ and $$\Delta ADY\sim \Delta XCY.$$ So we have $$\frac{BK}{DY}=\frac{XK}{LY}$$ and $$\frac{DY}{CY}=\frac{AD}{XC}=\frac{AY}{XY}.$$ Hence $$\frac{BK}{CY}=\frac{AD}{XC}\times \frac{XK}{LY}\implies \frac{BK}{BC}=\frac{CY}{XC}\times \frac{XK}{LY}=\frac{AB}{BC}\times \frac{XK}{LY} $$ $$\frac{AB}{LY}\times \frac{XK}{BK}=\frac{AB}{LY}\times \frac{LY}{DY}=\frac{AB}{DL}$$ $$\implies \Delta CBK\sim \Delta LDK$$ And we are done. We get that $$\angle KCL=360-(\angle ACB+\angle DKC+\angle BCK)=\angle DAB/2 +180-\angle DAB=180-\angle DAB/2$$ Motivation: I took a hint on this. I had other angles but I did...

IMO 2023 P2

IMO 2023 P2 Well, IMO 2023 Day 1 problems are out and I thought of trying the geometry problem which was P2. Problem: Let $ABC$ be an acute-angled triangle with $AB < AC$. Let $\Omega$ be the circumcircle of $ABC$. Let $S$ be the midpoint of the arc $CB$ of $\Omega$ containing $A$. The perpendicular from $A$ to $BC$ meets $BS$ at $D$ and meets $\Omega$ again at $E \neq A$. The line through $D$ parallel to $BC$ meets line $BE$ at $L$. Denote the circumcircle of triangle $BDL$ by $\omega$. Let $\omega$ meet $\Omega$ again at $P \neq B$. Prove that the line tangent to $\omega$ at $P$ meets line $BS$ on the internal angle bisector of $\angle BAC$. Well, here's my proof, but I would rather call this my rough work tbh. There are comments in the end! Proof Define $A'$ as the antipode of $A$. And redefine $P=A'D\cap (ABC)$. Define $L=SP\cap (PDB)$. Claim1: $L-B-E$ collinear Proof: Note that $$\angle SCA=\angle SCB-\angle ACB=90-A/2-C.$$ So $$\angle SPA=90-A/2-C\implies \ang...

Just spam combo problems cause why not

This post is mainly for Rohan Bhaiya. He gave me/EGMO contestants a lot and lots of problems. Here are solutions to a very few of them. To Rohan Bhaiya: I just wrote the sketch/proofs here cause why not :P. I did a few more extra problems so yeah. I sort of sorted the problems into different sub-areas, but it's just better to try all of them! I did try some more combo problems outside this but I tried them in my tablet and worked there itself. So latexing was tough. Algorithms "Just find the algorithm" they said and they died. References: Algorithms Pset by Abhay Bestrapalli Algorithms by Cody Johnson Problem1: Suppose the positive integer $n$ is odd. First Al writes the numbers $1, 2,\dots, 2n$ on the blackboard. Then he picks any two numbers $a, b$ erases them, and writes, instead, $|a - b|$. Prove that an odd number will remain at the end. Proof: Well, we go $\mod 2$. Note that $$|a-b|\equiv a+b\mod 2\implies \text{ the final number is }1+2+\dots ...

Sunaina thinks absurd

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