Processing math: 100%
Skip to main content

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 will post , so if you are interested, then do subscribe 😄 , so that you don't miss out anything new!

Also I am Sunaina Pati in MSE and Jelena_ivanchic in AOPS.


See y'all soon! 

Sunaina 💜

Comments

  1. Replies
    1. Sunaina didi (I'm not sure if you're older than me but nvm), saw you in the qualifiers' list to APMO. Congrats!

      Delete
    2. Haiii Thanku uwu.. I am older than most of the people so a very high chance that I am your senior :P..

      Delete
  2. Nice! Looking forward for interesting posts 😀
    #godyaarproyaar

    ReplyDelete
  3. I like to solve almost all problems by myself and not see the solutions, i still haven't done all your MSE questions :\ Anyways, looking forward to more interesting questions!

    ReplyDelete
    Replies
    1. oopsie, now I am trying to guess who you are :P.. well I won't post solutions, cause they are bit more time taking, I write walkthroughs , but yeah trying problem urself is the best, One can refer walkthroughs for hints , cause solutions might reveal spoilers . Thanks for the comment! :) .

      Delete
    2. For the discord id, we need the full id, name+ 4 digit tag, hope you add it soon

      Delete
    3. I think AOPS is fine for contacting!! So, ig Discord isn't needed! :)

      Delete
  4. Yeah AOPS is more than enough to contact, i just wanted to let you know that you hadn't put the whole of it there ;)

    ReplyDelete
  5. Ayo finally landed

    ReplyDelete

Post a Comment

Popular posts from this blog

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...

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...

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....

Some problems in Olympiad Graph theory!

Hello there! It has been a long time since I uploaded a post here. I recently took a class at the European Girls' Mathematical Olympiad Training Camp 2024, held at CMI. Here are a few problems that I discussed! My main references were Po-Shen Loh's Graph theory Problem set (2008), Adrian tang's Graph theory problem set (2012) and Warut Suksompong's Graph Cycles and Olympiad Problems Handout and AoPS. I also referred to Evan Chen's Graph theory Otis Problem set for nice problems! Text Book Problems which are decent A connected graph G is said to be k-vertex-connected (or k-connected) if it has more than k vertices and remains connected whenever fewer than k vertices are removed. Show that every k-connected graph of order atleast 2k contains a cycle of length at least 2k. We begin with a lemma. Prove that a graph G of order n \geq 2k is k connected then every 2 disjoint set V_1 and V_2 of k distinct vertices each, there exist k...

Orders and Primitive roots

 Theory  We know what Fermat's little theorem states. If p is a prime number, then for any integer a, the number a^p − a is an integer multiple of p. In the notation of modular arithmetic, this is expressed as a^{p}\equiv a{\pmod {p}}.
So, essentially, for every (a,m)=1, {a}^{\phi (m)}\equiv 1 \pmod {m}. But \phi (m) isn't necessarily the smallest exponent. For example, we know 4^{12}\equiv 1\mod 13 but so is 4^6. So, we care about the "smallest" exponent d such that a^d\equiv 1\mod m given (a,m)=1.  Orders Given a prime p, the order of an integer a modulo p, p\nmid a, is the smallest positive integer d, such that a^d \equiv 1 \pmod p. This is denoted \text{ord}_p(a) = d. If p is a primes and p\nmid a, let d be order of a mod p. Then a^n\equiv 1\pmod p\implies d|n. Let n=pd+r, r\ll d. Which implies a^r\equiv 1\pmod p. But d is the smallest natural number. So r=0. So d|n. Show that n divid...

Let's complex bash Part 1

I have to learn complex bash. And almost everyone knows that I am notes taking girl so thought why not make a post on complex bash ( so that I don't get emotionally demotivated lol).😇 There wasn't any need for learning complex bash, but it was in my dream checklist i.e " To learn a bash." And since I am not loaded with exams, I think it's high time to learn Bash and new topics.  Also if anyone from the "anti-bash" community is reading, sorry in advance and R.I.P.  Notes:- 1. Complex numbers are of the form z=a+ib, where a and b are real numbers and i^2=-1. 2. In polar form, z=r(\cos \theta+~~i\sin\theta)=~~re^{i\theta}, where r=~~|z|=~~\sqrt{a^2+b^2}, which is called the magnitude. 3. Here we used euler's formula i.e \cos \theta+~~i\sin\theta=~~e^{i\theta}. 4. The \theta is called the argument of z, denored \arg z. ( \theta can be considered in \mod 360 and it is  measured anti-clockwise). 5. The complex conjugate of z is ...

Problems I did this week [Jan8-Jan14]

Yeyy!! I am being so consistent with my posts~~ Here are a few problems I did the past week and yeah INMO going to happen soon :) All the best to everyone who is writing!  I wont be trying any new problems and will simply revise stuffs :) Some problems here are hard. Try them yourself and yeah~~Solutions (with sources) are given at the end! Problems discussed in the blog post Problem1: Let ABC be a triangle whose incircle \omega touches sides BC, CA, AB at D,E,F respectively. Let H be the orthocenter of DEF and let altitude DH intersect \omega again at P and EF intersect BC at L. Let the circumcircle of BPC intersect \omega again at X. Prove that points L,D,H,X are concyclic. Problem 2: Let ABCD be a convex quadrangle, P the intersection of lines AB and CD, Q the intersection of lines AD and BC and O the intersection of diagonals AC and BD. Show that if \angle POQ= 90^\circ then PO is the bisector of \angle AOD ...

New year with a new beginning! And a recap of 2024..and all the best for INMO 2025!

Hi everyone! Happy New Year :)  Thank you so much for 95k+ views!!! How was everyone's 2024? What are everyone's resolutions? ( Do write down in the comment section! And you can come back 1 year later to see if you made them possible!). A Better Mathematician  Well, technically a theoretical computer scientist.  I am so grateful to be allowed to study at CMI where I can interact with so many brilliant professors, access the beautiful library and obviously discuss mathematics ( sometimes non math too ) with the students.    And this year, I want to learn more mathematics and clear my fundamentals. I have become much worse in math actually. And hopefully, read some research papers too :)  And discuss a lot of mathematics with other people.  However, with that whole depressing 2024 year, I have lost a lot of my confidence in mathematics. And to be a better mathematician, I should gain the confidence that I can be a mathematician. And well, I am working on...

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...