day 10 3:32 am, 6 october 2025 every single moment. cos i wanna be the best there has ever been go win smmc now. it’ll happen iff you work every single moment frm now uptill 11 october. fuck nigga lets fucking goooooooogt4oiphji. $R(3,t) ~ \frac{t^2}{log t} \iff \alpha(G) ~ \Theta(sqrt(nlogn))$ for triangle free $G$. This statement is essentially equivalent to $n = \Theta(\frac{t^2}{logt}) \iff t = \Theta(sqrt(nlogn)$ pretty cool, the main idea then is just to prove log t ~ (log n)/2 yup my intuition just got better ahh i remember reading this theta stuff in clrs bruh. come on man , i wanna learn so much interesting stuff and do so much intersting stuff ahhhhhhh lets keep going . 5:19 am damn i wanna do lots of stuff before smmc, the point is really, im just very smart, but i deserve to win iff i work every single moment right. so what you study doesnt really matter, what really matters is you do “something” every single moment. right now im tired asf, so i guess ill revise enumerative combo and diestle before going to sleep. i mean ok, the point is i can prolly alraedy do most of the problems, i just wanna feel so fucking confident and arrogant tho, and like i wanna learn so much cool stuff and achieve so many things, the only way to do that is to push myself so much, so ive made a deal w myself which is like, youll win smmc, asia #1 if you work every single moment between now and then. woohoo. 6:20 am revised everyhting up till cycles from stanley’s enumerative combo… ahhh revising stuff is really fucking boring but i have to do it. this image is my wallpaper now… it’s really that simple, work every single moment of your life and all your dreams are coming true. its really that simple man. lets keep going. literally cos, if i just work these 6 (5?) days non stop, i am winning smmc. what a sweet fucking deal. no way youre gonna mess thsi up. no way im gonna lose man. literally no fucking way i dont win smmc. literally no way im going to stop at all. just do not stop. uhhh ill do the rest of enumerative combo revision sometime else; lets do a bit of diestel right now, just so my “surface area” of things to do increases. then i might do a little apostol and mont before going to sleep. just keep working. who tf cares if its boring, i need to do this shit. 6:31 am man looking at diestel is really really really fucking pissing me off. im supposed to have done all this shit. like i always imagine myself as reading lots of cool math, learning so much stuff. solving difficult problems right. no way you can waste a single second let alone a day man. im telling you this time ive started this journey thats not going to stop at all. just keep going and keep the momentum building man. lets go bruh… lets keep going. 7:14 am ok i completed almost the whole of chapter 1 of diestel, like i guess everyhting till normal trees. ill do the rest later. again i just wanna increase my surface area right now… im telling you man, im going to get this. honestly smmc aint shit at all. im going to own this world, smmc really aint nothing. but its just a fact that if i work every single moment frm now till then i will win it. like thats just a fact man. just have fun with this shit. once its over, guess what, we’re still gonna keep wokring exactly like this. yuh, we like that man. lets fucking keep going bruh… all the way up… i guess i wanna do some apostol ? cos like listen, im studying math. idgaf about smmc, i aint finna sit here and study for smmc when i wanna change the world, ill study wtv the fuck i want to, but the point is ill study all day! ill think hard all day, with some breaks of “simple” thinking in between. yuh. im just not gonna stop. apostol here we go. like listen this is the cool part about math. if youre a genius like me, you can solve any problem. so its not like i need to learn any specific thing, this is just a challenge for me to start working hard and get the journey started hoestly , cos ive taken too many L’s. egooooo. arrogance. lets fucking go. 8:02 am we just completed complete revision of apostol ch-2 also! woohoo lets keep this ship rolling. imma do a little bit of mont before going to sleep lesgo gng. 8:08 am in 5 mins i just looked through the whole of MONT chapter 1. damn that’s crazy. well i need to go sleep now. tomorrow i need to work this hard also, like all day tomorrow too, and i guess to start me off, ill do a mock exam in the morning, just to get this shit started quick… lemme go make me a mock woohoo and then go to sleep. night night gng. 11:27 pm 6 october well, im proud of myself for this one. i woke up at like 6ish pm, and i went straight to work. like i really was like nah i aint doing nothing. no instagram, no whatsapp, no complacence. i aint let myself convince me its ok to waste a little time. I had generated a paper last night, I started doing it at like 7ish pm. question paper ok so this was not a good test but im still proud of myself for not stopping. i wanst feeling like my usual sharp self. couldnt think straight but i still kept pushing and kept thinking. problem 1 i could not think of any good construction at all. no idea how to solve. after 30ish minnutes, i switched to problem 2. here i immdeately knew what to do, like i constructed the sum pretty quickly. all that was left is to find it. and then i found a really cool solution using symmetric sums and stuff. it took me like 20ish minutes to get the main idea. then i left the details for later. in problem 3, i proved some cool things like P(0)=0 and P(x)=P(-x) I then put P(x)=Q(x^2) I thought i was so fucking close to being done cos you get something like Q(x)+Q(y)+Q(z)=2Q((x+y+z)/2)) i was getting kinda annoyed tbh, cos i couldnt formulate it exactly, but wtv thought for some time, couldnt really think at all. Then i just converted this problem to a 1 variable equation by putitng c=1 and finding b=f(a). Then i got the idea of saying let P(x)=x^2n+c*x^(2n-2)+... and looking at coefficient of x^(n-2) in the two equations. but i was mesing up the calculation again and again so i thoguht to switch to problem 1. I proved that there is a maximal solution to this problem which is sorted. like the numbers are going to be sorted. this was cool so then say i occurs x_i times. (cos if you have numbers bigger than n it’s a waste) then we just wanna maximise $\sum_{i=1}^{n-2} x_{i} x_{i+1} x_{i+2}$ given $\sum x_{i} = n$ here i finally got the answer, to be 667^3. but i couldnt think of any solution at all. like i couldnt think of how to prove this inequality at all. then it was like 9:45 ; so technically just 15 minutes left. started writing solutions, wrote out p2 pretty quickly. startdewriting p3, and just completely messed up the calculation. switched to p1, and while writing the solution i finally got the idea; which is to induct on $n$ to prove if $\sum_{i=1}^{n} x_i =r$ then max of $\sum_{i=1}^{n-2} x_{i} x_{i+1} x_{i+2}$ occurs when x_1=x_2=x_3=r/3 and everything else is 0. for n=3 it is obvious, now by induction; look at $x_{n-3} x_{n-2} x_{n-1} + x_{n-2} x_{n-1} x_{n}$ Just see that the transormation $x_n \rightarrow 0$ and $x_{n-3} \rightarrow x_{n-3}+x_{n}$ increases the sum. So we’re done. then i switched to P3 again; finally got the calculations to work. I thought the answer was supposed to be just n=1; ie. P = x^2; but in the equation i got n=2 works. I was confused but then i realised that i had neglected constant terms, so if n=1; 2n-2 is the constant terms. anyways, my equation proved n <=2 So P(x)=x^4 + bx^2 but here i still thoguht only x^2 worked, so i found a “counterexample” for x^4; something liek 2,2,-1 (whch actually works haha) cos like time was less. so i said only x^2 works. i mean its obv (i just proved it now) that x^4 also works, so i mean yeah. solutions bruh i aint even get to think about problem 4 damn man, i wanna be able to solve imo 3’s dont be scared of this stuff, just tihnk and youll probably solve it lol. this was cool, i didnt give up till then end and i worked hard. wtv this was just a mock, the fact is the deal is already made. if i just keep wokring non stop i will win smmc for a fact. I am the goat nigga, come suck my dick bitch ahhhh. Then when i was done with this, Sagnik had sent a problem. i didnt feel like thinking about it, but still i did, and i found a brilliant solution. my solution was that say you do the ith centered flip x_i times (so like x_4=1 means i did the operation x_3,x_4,x_5 flip once) and so on number the numbers starting at 0 (a_0,a_1…a_n-1) so the problem is reformulated as finding x_i such that x_{i-1}+x_i+x_{i+1} is odd if and only if i=0 there’s only finite possible x_-1 x_0 x_1 values possible ; and if you fix these values the whole thing is fixed and you can see what works; so like if they are 1,1,1 then you’ll see x_2 must be 0; then x_3 must be 1; then x_4 must be 1; then x_5 must be 0; so it’s periodic and this implies n-2=2 mod 3; or n=1 mod 3 and then look at all constructions, they’ll work for some n mod 3 and you’re donezo. yuh man we aint stopping at all, we’re gonna keep studying. im coming back from a scooty ride, i swear imma keep going. i cannot stop bruh, i really am not going to stop. if you just do this, im winning for a fact, so all you gotta do is just keep studying. lets fucking go man. im just not going to stop. lets work bro. lets fucking work. i am going to win this. asia number 1. this si just the start of the rise of mony. this is my world bitch. lets have fun yall just witness history 1:28 am i have a sort of list of things i wanna study rn: Stanley enumerative combo, diestel, Alon and spencer, MONT, apostol, Putnam and beyond, Summation handout, Ineq handout, FuncEq handout, Probabilistic handout, yufei zhao i really wasnt sure what to do rn, i mnea thething is i gotta revise en. combo, diestel (lil) , MONT, apostol before i can moev ahead (do I???). but right now im fresh, so i dont wanna waste time revising stuff when thats something i can do when bored also. idk what to dooooo. i was revising stanley but i felt so bored. ahhhh. im not gonna stop, thats the thing tho, i guess lets do some more interesting thing. im watching yufei zhao’s lecture for a little while first. 1:42 am So i know a couple mantel theorem proofs: (writing them from memory here): (mantel says max edges in triangle free graph is n^2/4 ; bipartite graph with two parts of ’same’ size) ie. max edges in triangle free graph; you say d(x)+d(y) \le n whenever x,y is an edge; then you look at $\sum d(x)^2= \sum_{e} d(x)+d(y) $ and rhs is atmost $mn$ (m is number of edges) and rihgt hand side is atleast (2m)^2 / n which gives you mantel bound another proof is: Let A be the maximal independent set. neighbours of v are always an independent set; so d(v) \le |A| Let B=V/A ; ie. the complement of A Then each edge must pass through B. So, number of edges $m \le \sum_{b \in B} d(b) \le |A||B| \le (\frac{|A|+|B|}{2})^2 =\frac{n^2}{4}$ donezo Then there’s Turan’s theorem; ie. max edges in $K_{r+1}$ free graph is e(T_{n,r}) which is the complete multipartite graph, with r parts, each part of roughly same size. first this is equivalent to; any graph has an independent set of size atleast $\frac{n}{d+1}$ where d is ofc avg degree; cos you just apply this for complement fo graph. One proof is ofcourse the brilliant probabilistic proof; ie. you order the vertices randomly, and contruct an independent set as: add v in the set S if and only if all vertices to the left of v are non neighbours of v; or you can say all neighbours of v are to the right of v. So, then $r \ge E[S]=\sum_{v} Pr(v \in S) = \sum_{v} \frac{1}{1+d(v)} \ge \frac{n}{1+\frac{2m}{n}}$ which rearranges to give $m \ge (1-\frac{1}{r}) \frac{n^2}{2}$ GG Another proof is to induct on n right. So consider a maximal graph; it must have a $K_r$; say it is $A$ let $B$ be it’s complement. each vertex in $B$ has at max r-1 neighbours in $A$. So then our graph has $m=e(A)+e(B)+$ edges between A and B The first term is just $\binom{r}{2}$ The second term is atmax $e(T_{n-r,r})$ and the third term is at max (r-1)(n-r) and you can prove this is at max e(T_{n,r}) (each term also follows from equality case) Last proof is the Zykov symmetrization thingy; Which says again consider Maximal graph. Then it says that non edges of G form an equivalence relation; ie. if xy and yz are non edges, xz must be a non edge also. The proof is to assume xy and yz are non edges but xz is an edge. Then you see if d(x)>d(y) you can replace y with a “clone” of x and still remain with a $K_{r+1}$ free graph but this one has more edges. and on the other hand if d(y)>=d(x) and d(z) ; you can replace x and z with clones of $y$ and still remain K sub r+1 free but have more edges. So, complement of G is a graph whose components are complete graphs; we wanna minimise the number of edges in this; and you can do this by jensen. first off there’s at max r components; so just use jensen and you’re done. you can also look at G, adn say its complete multipartitie right, of at max r components, now is A and B have size difference more than 1; you can put a vertex from larger set in the smaller set and number of edges will increaes contradicition; so again all sets are roughly the same size, ergo, Turan’s graph Damn I remember all these proofs, thats crazy haha. Now the crazy part is, these are ok wtv proofs; but now if you wanna look at ex(n,H) that is max edges in a graph (with n edges) that does not have H as a subgraph; the answer is again just turan; like if H has chromatic number = 1+r; the highest order term is apparently just $(1-\frac{1}{r}+o(1))\binom{n}{2}$ which is genuinely batshit crazy wtf, thats actually soooooo cool damnnn cos i mean ofc ex(n,H) is atleast e(T_{n,r}) cos T_{n,r} is H free (cos chromatic number of Turan grpah is r; while H is 1+r; so it cant be inside T!) But like yeah the fact that it is exactly that is kinda crazy. lets see why yufei zhao is so cool man, like this lecture is genuinely so much fun ahahah 2:21 am ok so apparently erdos stone proved the result for complete multipartite graphs; and this is apparently elementary. and also simonovits proved this is enough for all H. ok this is a cool problem to work on later. ahhhh this is so good, im not stopping i really felt like taking a small break, maybe just looking at whatsapp or instagram, i was telling myself its ok, its not a big deal, but i was just like nah, i aint stopping haha. yeah we’re just not going to stop. like be fucking excited, cos the fact is if you just keep working just like 5 more days, im wiining smmc, and then imma keep winning and ahcieve all my dreams cos imma keep working hard right. like this is seriously so inspirational. 2:36 i was just thinking what to do i opened thomas calculus, there i found the page where i had solved my first informatics problem, damn. i coulda been imo gold and ioi gold. im not cos of me. theres no way imma have any regrets man, theres actually no way. go have fun man, and just work. cos work every single moment and all your dreams are coming true, like just 5 days the start of your dream is happening. ill win smmc if i work every single moment. what a crazy deal man, go make the best use of this shit. lets fucking go!!! nah wtf i remember i was sooooooooooo fucking sad the day my olypiad journey had ended i have a perfect opportunity to study cool olympiad math right here man wtf like actually this is crazy. i have literally the perfect opportunity right here. lolll lets fucking go get it. litlle kid in lucknow who started this joruney thekid in gurgaon who saw the dreams make them proud right here man go work hard every single moment and achieve all your dreams. Summation handout. 4:39 am nah took a break but how can you not put every single ounce of effort into gettting this no way nigga my jannik sinner getting ranked moment smmc right here best in asia go get it