Skip to main content

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 have got into the team, I would have left math". I felt my whole hard work was wasted. I have realised that hard work to some extent helps you in Olys but in the end, you really have to be smart( Not dumb like me). 

My mental state after EGMO TSTs was horrible. I really left olympiad math, didn't do any problem on my own and had this negative vibe. I am so lucky to have my parents to support me :D... 

But then I thought about the grade 5 Sunaina, who literally thought that she can not even get state rank 1 in her state MO. Even 10th Sunaina didn't expect to qualify INMO.  Making the EGMO team was my dream, but honestly, I wanted to make the team just to make new friends. To talk with similar brilliant young Indian females. But thanks to sophie fellowship, OTIS and AoPS, making EGMO wasn't needed anymore.

Yes representing your country is such a big deal, but honestly, I think it's better to not try Olys in 12 anymore. Quite a big decision, but yes. Does the mean no more oly blogpost? Definitely not. But the problems will simply be my tastes :P

Am I sure? Yep! I have already talked with my friends, and my parents and currently talking with you all. Who else should I tell? :P

What will you do then? Spend my last year of high school at school, do my internship, explore new math, and skincare, expand my math club called philomath club, and be stress-free. 

A small piece of advice to other fellow aspirants: Just make sure to enjoy Olympiads but please don't bunk school. Don't. Schools are important and simply enjoy life :D..
And at least if you writing TSTs, getting a bad score is still fine! You learn from it, right?

I am not leaving Olys because of my bad TST score but just to explore more math. Like, learn Real Analysis, Abstract Algebra, etc. Very Fancy.


But what actually happened in TSTs? I never actually talked about it :( But, sure I think it is the right time to share!

Day 1

So day 1 of TSTs, my house condition wasn't nice, in fact, I had a fight with my parents just hours before my TSTs. I really do not know what happened that day, but now thinking over it, it was probably me being very stressed out as the reason for the argument was very stupid. 

But after the argument, I realised that, no, this is not good, my whole day would go bad as I had a fight, etc etc, and more and more stress built up. 

Skip to an hour before the TSTs, I was talking with  Rohan Bhaiya and he was asking me to calm down. The next thing was logging into the special portal HBCSE made for the EGMO TST contestants, where we could access the questions and then upload our scanned solutions. 

Now, before logging in, I thought" WOOOPSI, I have not revised ineqs". So I opened OTIS excerpts and revised ineqs and my bad luck, I skipped weight am-gm! Anyways, after revising and keeping my chocolates aside, my mind simply froze when I saw P1.  P1 of Day 1 was simply weighted am-gm. I knew it once I saw it, but then I was like" OH F, what was weighted AM-GM? What was the formula?" I was trying to recall it, which was a big mistake, deriving it is like 10 seconds! HUGE HUGE stress. Anyways, I eventually gave up on trying to find what was weighted am-gm and wrote some Titu ineqs stuff ( which after the exam I realised were wrong, since I reversed the ineq signs)

P2 was hard but definitely interesting. I liked to try it as it was fun. Still didn't make sufficient progress. Using bezout's gave me 1 mark, so I got 1 mark in it.

P3 was actually very hard, rg said it was IMO P2/ P3 level. That's why Day 1 was soo hard! Plus plus I misread it :) 

Oh, and misreading a problem is a very common mistake of mine. I have done it thousand times tbh ( you will get to know where else :P)

Anyways, day 1 was the worst of the worst paper I ever had in my whole entire.


After day 1

I expected it to go bad, so I was mentally prepared and was ready not to cry, but idk why I was crying as hell and was very angry on myself. So many people tried to calm me down, said it was day 1 only, I still have day 2 left. I did have some hopes left as when I mocked last year EGMO TSTs I got all three prs :P. 

But, I kinda knew it was impossible seeing other people's performances, so during the 7 days gap between day 1 and day 2 of TSTs, I watched kdrama, relaxed and enjoyed math.


Day 2

I didn't care much about Day2, and IMO it went well, however, it was harder than day 1 ( as in p1,p2 were hard), so scoring there was very impossible. Hence I got no marks that day :(

I could have done the geo as it was fulllyy my type but thanks to ggb, I really could not proceed further. Rohan bhaiya said, my ideas were right but I should try them for more time. 

Yeah, so that's how my day 2 went :P

So yeah, that's how I temporarily lost interest in olympiads in general. It's because I thought I can not do well. All that happened was pure sheer luck :(

So after TSTs, I did not work that much for INMO, but rather covered my school math syllabus, studied chem, did FEs ( and became comfortable in solving them) and did a few mocks made by Sophie. 

Even just before INMO, negative thoughts were going through my head. For example, "Listen Sunaina, whatever happens, it's fine. You have not worked hard, so even if the outcome is negative, you don't deserve to be sad. " And then while I was thinking this, I as usual realised that I have not revised Geo lemmas, ineqs and fe properties. Even NT too!

I highly advise not to do this, but I still revised. :P

Another reason for me thinking this negative was me losing all my confidence, believing that I just got fortunate in INMO 2021 and somehow managed to solve P1. 

During INMO

I won't describe IOQM Part A, as I really didn't care about it. I knew that IMO team was almost impossible to make this year and hence Part A is useless ( yet I got 15 marks, which is apparently greater than Assam's cutoff :P)

I did P1 in 1.25 hrs. And I tried p2 but did some silly calculations, due to which I couldn't guess the $\pmod 3$ and then misread p3 :). Thank you. I am officially done. 

I actually did not write a neat solution for P1, in fact, I didn't even write the solution of P1. My rough progress was pretty neat enough to be sent. ( I might have ended up 1 mark hear).

For example, my "rough work" which I sent to HBCSE also had my thought process. etc etc.


Bits of Advice

1. Try to be $very^{\infty}$ calm

2. Don't try to revise like just beforehand

3. Ineqs suck

4. It's okay to forget formulas, but try to not remember formulas, remember how they are derived :)


Thoughts right after INMO

I was proud of myself. Like very proud of myself. I could do 1 problem in INMO, which is very nice. At least for me, since I thought INMO 2021 was simply me getting lucky. This year's INMO made me realise that I am both stupid and okay in Olys. Okay in Olys since I solved P1 and stupid since I made huge sillies!! Like c'mon I misread P3 ( I left one condition), else had things gone well, I would have got 17+3=20 in INMO :(

Right after the exam ended, I immediately thought, "Broooo, what if the paper was easy?". After I discussed the paper with Ananda ( who was sitting just in front of me in the test centre) coming out of the centre, I quickly discussed the paper with him and turns out he also did P1 only. So I have not performed that bad? 

Anyways calming myself down, I talked with my mother who was waiting outside. When I told her I did 1 problem, she was pretty happy ( at least 1 problem hua)!!

After that I called Rohan bhaiya and discussed my paper with him, he said that I have a huge chance of qualifying for TC. Then I called Pranav and talked with him and he did P3, I was like WOW 'cause solving P3 is just so waohaa as it was very hard.

Then talked with Gunjan, Swastika and more! 

Talking with a lot of people turns out almost everyone did 1 problem. And I was like so sad :( ( ofc I am happy for them but sad that there is a huge chance I might not qualify) and my last hope was girl's quota. :(

Anyways, asking tons of people about "the expect girl's quota cut off", I only knew 1 person apart from me who was eligible for the girl's quota and that was Gunjan who literally aced INMO! So she won't need a girl's quota.

After a few analyses, I gave up. Why would I care so much for an olympiad I didn't even work hard for. I was literally doing Sharygin problems days before INMO -___-

I had already accepted my defeat.


The day


The day when the results came out, I had another fight with my brother and very badly misbehaved with him :( sorry suhan :P

Anyways, in a bad mood, I opened Whatsapp and saw so many mssges. Realising that it's the day, I was $super~duper^{\infty}$ scared. I thought why today, I am going to get punished for behaving so badly with suhan. Anyways, so I immediately messaged Rohan Bhaiya and made a meet, 'cause I wanted to check my results with him. He is good luck, u know?

While checking, I forgot the email I gave while registering, so that made me more tensed! Anyways after Rohan bhaiya started getting annoyed, I immediately checked it and realised," I got 17! Phew! I got 17, that's nice I got full mark for P1, yeeyy! " was what I thought then saw, marks distribution, which literally surprised me!

" 16|0|1" I screamed ( but lowly, since my parents didn't know that results were out)! HBCSE what scam did u do with me, I was a sweet innocent kid :(

Anyways, I was still happy with my marks!!



The Cut-Off Predictions


This was so traumatic, everyone said cut off would be 17 or 20, some said 21 or even more. I was like, oh no, there goes my EGMO! Time to do Jee :(

After the reevaluation date passed, literally every day I was checking the website, refreshing so many times, the curiosity to know whether I am in the TC or not killed me :(

Again, losing hopes, I simply just lost interest in refreshing.

Now, one fine day, I was sleeping in the evening ( which for context I always do, I sleep a lot 'cause I am sunaina+lot=sloth) :)

So, yes, I was sleeping, my mom screamed and said INMO out! And I was like she is again scamming me because she has played this trick a lot to wake me up :-_-:

Anyways, she again said, and I was like "FINE I AM GETTING UP!" and she was like, "no it's really out" and I am like "oh, weird"

And after seeing cut off! I was definitely high! I QUALIFIED THROUGH THE GENERAL QUOTA!!! First thing I did was? Guess, guess!

Yes! Called Rohan Bhaiya~~

Anyways, that's how my INMO story wraps up!

If you still wonder why cutoffs were way lower than everyone expected, then notice that the people around you are not regular people ( as in they are not the general public )

I thought to make a kind of improvement table!

2018-2019[ grade 8]: Cleared PRMO, Cleared RMO, 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], Wrote EGMO 2022 TST[ Rank 8]

2021-2022[grade 11]: Qualified for IOQM part B directly, Cleared IOQM-B ( i.e INMO) [Through general quota]

Table 2021-2022 isn't completed, so I hope it improves even more :)



Additional Life update

The blog has a few more updates so do check them i.e two new pages have been added! How are they? I am also part of Sophie cohort 2 too! And they are so so so organised than last year! Very nice!!! I am also going to give my own tiny talk there. The kids are fine too, but some issues are there. I will talk about it later in the blog post. My father is also a BTS ARMY now :P. He particularly loves RM ( the leader of BTS ) and My mom has started watching "True beauty" with me! I think I am slowly and slowly challenging their viewpoints! 

My mom even commented on the type of guys I love and said " I know you love chocolate guys." Well, she is my mom in the end and definitely knows me well :P 

I watched the k-drama School 2021 and it's very very very nice! I really loved it, however, the plot was a bit similar to the "True beauty" plot.

But I really loved their music! In particular, I love the following one, you guys should try it :) 


 


All hail Sir Soobin

Next, I think I have started getting more into Tomorrow x Together, a kpop group! I really really love the member Soobin :D

Some Soobin Pics I love :) 

                                      







OMC Blog 

I am now part of the OMC blogger team ( I am actually the supervisor :P) and please please please do check out the OMC blog here. It's an amazing blog, great content and definitely must read to all the Oly kids! The OMC Blog is an initiative to get many math bloggers together on one platform. Many people are good at math writing and communication and have blogs on AOPS and other websites. We want to give such people a larger combined audience alongside other resources. On the other side, we also want to bring lots of useful olympiad content together for readers..

Some people might not know about OMC. The Online Math Club is an initiative to reach high school students interested in math and give them a platform to learn more and interact with others. The Club aims to increase exposure to olympiad mathematics and advanced mathematics. And OMC is free and open to all!



I did an MBTI test!



Yes, you heard it right! I got to know that I am an INTJ-T. 



I was surprised by how accurate the results were! I felt I was getting to know myself better, also turns out INTJ-T women are actually unicorns (i.e very rare :P)

I am very introverted but that doesn't imply I have stage fear or any confidence issue, I do think a lot before talking to anyone who is not my friend, but If I am forced to interact with someone, I am fine with it. I personally prefer living in solitude rather than having friends and I would kill myself if I don't see any improvement in myself :) Moreover, I am a planner! 

About friends, I would love to give an essay on it. Remember it's coming from a person who is highly introverted.

Firstly, they are very much needed. Literally, they are! However, make sure to get the right ones, I know I know you can't "guess" who are good influences and who are bad influences, but gradually after time, you really are able to tell if you can guess or not. If you think they are not, start drifting away from them. 
In my opinion, having fewer friends is nice, you would genuinely have less toxicity in life✨✨

If somebody says bad about you, ignore them. If your friends are not inviting you out in some stuff, that clearly implies they don't like you as a friend, so please stop considering them as your friend. Happened to me too, I realised that the people I considered friends never considered me one, I was never able to take the hints they sent! Not inviting me out, them hanging around, etc. Let's not talk about them, hehe! 

And listen, it's completely fine to be way different from other people. I personally think I am very different from others, none of my Indian friends are hardcore kdrama or kpop lovers and simultaneously do math. Most of them don't even run a math blog. Many don't run their own math club ( which I do, so go check out https://thephillomathclub.weebly.com/). Most don't do digital art. Many don't agree on how handsome Soobin is! 

And it's completely fine. Everyone is different. Remember though, do not change yourself! Accept the persona you are born with it. 

 I probably don't have any person whom I can relate and share my side of the story, 'cause I doubt they will understand my problems. Moreover, I am a person who kind of really looks for the negative, which is not good but those negative kinds of stuff (at least for me) motivate me and push me!

But I really wished I had one person who could really understand what I am going through and not laugh at me, or do something else while listening to me. Just one person and that person would be my true best friend. 

My parents always ask me to go out, meet new people and do all the social stuffs. But I never found that something "useful". Friends are necessary but fake friends are never. 

What's Next?

I really do not know! I really want to enjoy my last year at school, do olys and give my best shot, clear my mathematics fundamentals, watch kdramas, stan TxT learn a new language and what not! I simply want to enjoy my life, mathematics is one way to! 

All I can assure is that a lot of posts would be coming 'cause I will again start doing olympiads seriously! Till then, stay tuned :)

See ya'll soon
Sunaina 💜


Comments

  1. Had fun reading the post! Best wishes for your upcoming EGMO TSTs👍👍

    ReplyDelete
    Replies
    1. Glad you enjoyed it! :) Thankyou so much Pratik :)

      Delete
    2. You shouldn't have crammed during egmo tsts. Ig you could have got into the team had
      you not crammed so hard. Bcoz I did the same thing in imotc last year( and guess what, before inmo 2024 lol) and I scored one of the worst scores in camp.

      Delete
  2. Very interesting blog, I wish I could write such posts :P Wishing you the best for your future :)

    ReplyDelete
  3. I got Problem 1 and Problem 3 (a and b) on INMO. Don't know the score, but I didn't clear the first part.

    ReplyDelete
  4. Congratulations on your success...and loving your style of writing....

    ReplyDelete
  5. Very great blog post!! Best of luck for your future

    ReplyDelete
  6. And One such Friend is Atul :) Glad that I found a kindred spirit today. Same pinch ;))

    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...

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....

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 ...