/sci/ - Science & Math

>>9862425
>anyone here smart enough to brave them?
No. See >>9860149

>>9862430
oh lol
pic related average poster who can't solve at least a single problem in that list

I can only solve Problem 1.

>>9862425
I'll try some of them in the morning. Miss me with that geometry shit though

>>9862425
Where is The Lord when you need him?

>>9862425
At a glance, I can solve (as in, I have a clear idea of how to approach the problems) all problems except (5) and (6), for which I have some ideas but I'm not sure if they'll work. I'll see if I can find the time to write full solutions for them.

>>9863493
I have to say, that's a pretty stark increase in difficulty between the first and second contest days.

>>9862450
Tried problem 2. Only found a solution for n = 3 lmao

>>9862425
Well I know the answer to Problem 2 is at least all n which are divisible by 3.
In this case you can choose a1 = 2 and a2 = -1, for example.

But there could be more n, who knows.
I can't prove there aren't.

Results are out:

Teams -
USA #1
Russia #2
China #3
Ukraine #4
Thailand #5
Taiwan #6
South Korea #7
Singapore #8
Poland #9
Indonesia #10

Individuals -
1. Agnijo Banerjee ("British" currynigger), James Lin (Amerimutt) with perfect scores
3. Mihir Anand Singhal (Amerimutt), with 40 points
4. Marat Abdrakhmanov (Russian Khazak/steppenigger), Shih-Yu Wang (Taiwanese ricenigger), with 39 points each
6. Jonas Walter (German snownigger), Naoki Kuroda (Japanese ricenigger), Jung-Tao Cheng (Taiwanese ricenigger), with 38 points each
9. Yiyi Chen (Chink ricenigger), with 37 points
10. Zexuan Ouyang (Chink ricenigger), Vincent Huang (Amerimutt), with 36 points each

>>9863785
Vaginas with (semi-)functional brains:

1. Yolrada Yongpisanpob (Thai cunt), 34 points
2. Dain Kim (Korean comfort woman), 31 points
3. Aruzhan Amanbayeva (Khazak slut), 29 points
4. Chatchanun Suriyaammaranon (Thai cunt), Alina Harbuzova (Ukrainian prostitute), 28 points each
6. Orsolya Lili Janzer (Hungarian cumdumpster), 26 points
7. Jelena Ivančić (Serbian hole), 25 points
8. Renad Abualjamal (Saudi niqabcunt), 24 points (imagine how frustrated these sandniggers are after the vagina in their team outscored all of them lmao)
9. Lucia Krajčoviechová (Slovak skank), 21 points
10. Tijana Babić (Bosnian cumrag), 20 points

>>9863792
Correction: one Saudi sandnigger managed to outscore the cunt (by 1 point, lmao)
As usual, no oogabooganigger managed to solve a problem. Why are these apes even in the contest? Free vacations?

>>9862425
These just make me sad

>>9863829
why?

>>9862425
who designed that horrible logo

>>9862425
I've been frying my brain over problem 1 for the past hour and a half and couldn't solve it. I can't even read my own notes at this point. My drawings are too busy. And it's the easiest, right?

I'm moving on to problem 2 for 1h30m now.

>>9863660
>In this case you can choose a1 = 2 and a2 = -1
This gives you an increasing sequence, since a4 = a5 = 1.

>>9864001
Don't worry, anon, I'm a brainlet too.

>>9864063
I put trying to solve problem 2 on hold because I realised I was making a lot of calculation mistakes so I went to the kitchen to cook meself some rice and I think I got an idea of how to solve problem 1. Will report back with results.

>>9863792
>sandnigger
why the racism?

>>9864091
I give up. I can't find the contradiction. I thought I had it at one point but I got lost in my notes again and couldn't backtrack.

>>9862425
I used to participate in these meme contests at my small country level back in my middle school years but never took it seriously though it was fun and I got some awards early on.

Is there any point in attempting to solve this shit in my free time with a sub-160 IQ? What are the math prerequisites?

>>9864587
>What are the math prerequisites?
"The content ranges from extremely difficult algebra and pre-calculus problems to problems on branches of mathematics not conventionally covered at school and often not at university level either, such as projective and complex geometry, functional equations, combinatorics, and well-grounded number theory, of which extensive knowledge of theorems is required. Calculus, though allowed in solutions, is never required, as there is a principle that anyone with a basic understanding of mathematics should understand the problems, even if the solutions require a great deal more knowledge. Supporters of this principle claim that this allows more universality and creates an incentive to find elegant, deceptively simple-looking problems which nevertheless require a certain level of ingenuity."

>>9863785
>>9863792
Can we please stop this meme that men are only superior physically?

>>9864548

>>9864848
No. I can beat the shit out of 99% of women

>>9864907
why does that imply DE and FG are parallel? I don't get it.
everything else is trivially true.

I found a livestream of the awards ceremony but it's in Romanian. Does anyone have an English language one? The imo2018.org page isn't streaming anyhing like they said they would.

>>9862425
>IMO 2018 problems have just been released
>He is not in a private mailing list getting the problems the exact day after the kids take the paper.

Top kek, how does it feel to be a brainlet? I had those papers the day they were given.

>>9863785
Why do you refer to Asian chinks by their race but to American chinks as "amerimutts"? They are pretty clearly all chinks and pajeets.

>>9865479
Damn, the facebook stream is also in Romanian. What's the point of streaming it online if you're going to use a language that is spoken by only 20 million people?

>>9865485
Well, that's the privilege of being the host country. Instead of being a fucking pussy and whining about it on the internet why don't you go get funding and then propose to HOST IT IN YOUR FUCKING ENGLISH SPEAKING COUNTRY YOU FUCKING CHEAP MOTHERFUCKER PIECE OF SHIT.

>mfw the people who go to these exams are well prepared in advance
Throw a normal high school graduate and he won't be able to solve 25% of this test.
>hurr durr muh kid is so smaart
Yeah he's not.

>>9865490
To be honest that is just trivial. You could be the greatest genius but still, you would not pass the IMO without training. There are more than 100 years of Olympiad culture now. There are so many things that you NEED to know to even be able to tackle the easiest of problems that appear in olympiads.

I doubt that even the greatest genius would, taking the IMO, discover on his own Vietas formulas in time to be able to solve the algebra problems.

>>9865492
That's what i'm saying, it reminds me of the middle-school math competition in the US i think, where 14yo kids would immediately hit the buzzer as soon as they saw the question because they have already tackled it before.
These "kid" are trained for these kind of problems, no critical thinking involved, no "pure skill", it looks nice on your CV sure, but in the real world with real problems this shit don't slide.

>>9865499
Well, no. You are going too far. You need to memorize a lot of shit but no IMO problem is ever routine. There is no way to solve any of these problems without thinking at least a bit ingeniously.

And trust me, I've seen kids tackle problems with machinery much more advanced than necessary and still fail to solve it.

>>9865488
Why are you yelling? Wouldn't it have been nice for the ceremony to be watched by the greatest possible number of people?

>>9865501
"competition math" and pure math have nothing in common, sorry to burst your bubble, the "tricks" you learn to quickly solve these problems won't ever be needed in real world engineering problem you may encounter.

>>9865519
Oh yes well when Romania hosts everyone like to complain. Well fuck you. It's not like you do anything special for us when YOU host. This year we host, so you get fucked. Don't like it? Host it yourself pussy.

>>9865525
Kek nobody gives a shit about you subhuman engineers. Why are you even in this thread? Don't you have a pile of shit to be rolling around you disgusting pig?

>>9865531
You need math in engineering.

>>9865532
You need disgusting cancerous brainlet tier math that even a monkey could learn after I hit it with a bat right to the brain 5 times to the point he is more deformed than the numerical methods you use, and then even that monkey would say that it was too trivial and would ask to please teach him something with actual substance.

>>9865533
But engineering helps solve actual problems, what will change if i solve the riemann zeta hypothesis?

>>9865528
It's constructive criticism you whiny gypsy.

>>9865535
>what will change if i solve the riemann zeta hypothesis?
What will change is that instead of feeling like an empty husk of a human being with no drive, you will finally have something to be proud of.

>But engineering helps solve actual problems
You solve actual problems by applying general methods that are known to always work. You literally do nothing at all. Not once in your life has your brain even had an original thought. You are a disgusting pig rolling around in the shit you call your engineering textbooks.

>>9865538
>You literally do nothing at all.
>Not once in your life has your brain even had an original thought.
https://interestingengineering.com/35-inventions-that-changed-the-world
huh

>>9865536
Oh, "constructive" criticism huh. Fuck you. Nobody cares for Romania when disgusting english speaking pieces of shit host. Nobody thinks about us. Then once in a billion year Romania gets to host and OH. OH. NOW IT IS A PROBLEM THAT THERE ARE NO TRANSLATION.

WOE IS ME! SOMEONE CREATE A CHANGE.ORG PAGE :(

When Romania host we think of our students. We do it for them. Romanian broadcast is for us, not you. Fuck you. Maybe if in the following years you are a bit more thoughtful with Romania, when we host it again we may hire translator for you. But until then fuck you.

>>9865542
>>9865538
samefag.

>>9865540
>I am this list of engineers that aren't me
Once again, the thought process of the modern engineer is able to amaze even the brightest minds.

>>9865544
>5544
>>9865533
>5533

The gods have spoken through the posts of this young schizophrenic. Engineers are monkeys and pigs. It is the word of GOD.

>>9865525
you gain a surprising amount of insight by solving olympiad problems, and you also get exposed to a lot of pure maths ideas you probably wouldn't see otherwise (think induction, infinite descent, considering degrees of freedom, p-adic valuations, etc.etc)

>>9865600
>induction
Everyone in middle school learns this

>>9862425

1. nicer problem than for the usual imo p1, but somewhat easier, took 30 minutes:

Let P, Q be the midpoints of AB, AC. Then the intersection of the perpendicular bisectors of AB and AC with the circle are the midpoints of minor arcs AB and AC. Since all lines DE described are all perpendicular to the angle bisector of angle BAC and since the line connecting the midpoint of arcs (call them M1, M2) is clearly perpendicular to it, we will prove that all lines FG are parallel to M1M2. This is equivalent to proving that FM1M2G is an isosceles trapezoid or that FM_1 =GM_2.

Now consider the midpoint of AB (call it R). It is easy to see that PR is half of AD is equal to half of AE is equal to QS, where S is the midpoint of AC.

Now rotate AB around the center until the center, P and Q are collinear (so that the image of AB is parallel to AC). Is is easy to see now that the arcs FM_1 and GM_2 have the same lengths, since their projections onto AB and AC have the same length starting from the midpoint.

>>9865606
sure, try this exercise then: prove that there are infinitely many pairs of positive integers (x,y) such that (x+1)/y + (y+1)/x=4
the point is also not simply the concepts learnt, but also the insight gained to truly understand them and apply them creatively

>>9862425
p2
motivation to following solution (as i believe is the one most people found?) is that periodic functions are only nice when you look at them globally and not locally, also the sequence is otherwise hard to track. i also know of at least one other person who just tried random algebraic manipulations until they hit this:

(not particularly inspiring)

rewrite the recurrence as a_ia_{i+1}a_{i+2}+a_{i+2}=a_{i+2}^2

sum across all indices i from 1 to n, and recalling that the sequence is periodic,

the left hand sum is equal to Sum from 1 to n of a_i(a_{i+1}a_{i+2}+1)= sum from 1 to n of a_ia_{i+3}

the right hand sum is equal to the sum from 1 to n of a_i^2.

multiplying both sides by two, we obtain the equivalent equality:

sum from 1 to n (a_i-a_{i+3})^2=0 or that a_i=a_{i+3} for all i.

it is clear that no constant sequence works (x^2-x+1 has no real solns) so we must have n divisible by 3.

For all such n divisible by 3, the following sequence works: (2,-1,-1,2,-1,-1, etc.)

>>9862425
p4:

the answer is K = 100.

To get the construction, simply colour the board in a chessboard fashion and Amy places on black squares every time. Since there are 200 black squares and no two are sqrt{5} apart, she can clearly always get at least 100.

We prove that she cannot do any better:
partition the board into 4x4 subgrids and consider the following cycles of points in each 4x4.

ABCD
CDAB
BADC
DCBA

it is clear that for each cycle denoted by a letter, Amy can place at most 1, since Ben can play the "opposite" square, so this gives an upper bound of 1/4x400=100

>>9862476
>Where is The Lord when you need him?
He keeps appearing in his own thread >>9865585.

>>9864548
I soldiered on with the livestream and saw a kid from Mexico fiddling with a similar drawing. I think he might be the one who only got 1 point on problem 1. I see he got bronze.

>>9865625
I got the same result through brute force. Didn't think of rewriting the recurrence formula like that. I wrote about 15 pages this morning. It took me 3 hours. So basically, an honourable mention is the best I could have hoped for.

>>9865608
correction to typos:
R is the midpoint of BD and S is the midpoint of CE

>>9863792
Alina Harbuzova and Jelena Ivancic are cute. By the way, why are the Mirzakhani prizes limited to one per continent? I mean, I get it that it's an affirmative action award, but the fact that higher scorers get cheated out because they're from the wrong continent makes it an even bigger joke. Don't they realise how counterproductive this is?

>>9863493
> I'll see if I can find the time to write full solutions for them.
It's the weekend. You have no excuse now. Post your solutions.

>>9865615
Not him but turned that problem into solving [math] 3a^2 - b^2 = 2 [/math] which is a trivial exercise in algebraic number theory. How to solve with elementary techniques?

>>9865686
rewrite as x^2-(4y-1)x+y^2+y=0
this is quadratic in x, so if (x,y) is a solution so are (4y-1-x,y) and (y, 4y-1-x)
inductively generate more from (1,1)

>>9865615
>ntegers (x,y) such that (x+1)/y + (y+1)/x=4
Okay, I tried this but I can only find a finite number of solutions? I think I can even prove that there are a finite number of solutions. I'm not denying that you learn new things by doing these problems but that still doesn't change the fact that induction is taught in middle school. I'm not the guy you were originally arguing with btw.

>>9865692
Ah man, I'm so dumb, obviously Vieta.

Interestingly, diophantine equations like these are disappearing from Olympiads. I think that equations with a finite number of solutions are favored nowadays.

>>9865694
>I think I can even prove that there are a finite number of solutions
Okay, just ignore this. The "proof" was wrong

>>9865615
I'm just a high school graduate but can't we re-write that as :
(x^2+x)+(y^2+y) congruent to 0 (mod 4)
Also we know that (x^2+x)=2k
and that (y^2+y)=2k
Is this a good start or?

>>9865315
The transversal created complimentary angles that are congruent so the lines are parallel

>USA
USA
>USA
USA

for number 4
a distance of exactly [math]\sqrt{5}[/math] with integer coordinates only can be achieved from coordinates [math](x_0+2,y_0+1),(x_0+2,y_0-1),(x_0+1,y_0+2),(x_0+1,y_0-2),(x_0-2,y_0+1),(x_0-2,y_0-1),(x_0-1,y_0+2)(x_0-1,y_0-2)[/math] so for each move the cunt takes, 8 to 9 other options close to her. starting from 400 possible options on move 1 to 392~391 for the second. The maximum amount of K moves in this theorical setting is [math]400/9 +1 = 45[/math] and the minimum is [/math]400/10+1=41[/math] due to how Ben can act like a little bitch.
So if you take into account that Ben is a little bitch (he is) the number of moves Amy can make before she's stuck is 41, Ben will likewise take 41 moves because he's that much of a little bitch. That's obviously wrong.

BUT, not all moves are created equal (t. some dumb bitch of the past, probably Ben's grand grand grand bitchdaddy or something) as a move on any corner only precludes Amy 1/4 of the moves, but Ben can be THE littlest bitch and put his first two moves on corners. So let's assume that moves that would preclude Amy the least amount of moves are Ben's top priority (he is a little bitch afterall, that's what he does). Any move in the area 1 unit from the sides only precludes her 4 moves, 2-3 units from the sides 6 moves and 4 units have the full amount of preclusion.

So let's break it down as thus. Starting at column 1, Amy places a point at one side, and ben, being a bitch, places it mirroring it at the opposite site of the column. This takes Amy to take 10 moves, and ben 10 (terrible cartoon, also a little bitch like this other ben) also. The same can be repeated by Amy on any column that is more than 2 away from any other column on which this is also happening AND partially on columns that are on ben's little bitch side of the columns. Given that, Amy can at least put 60 on the initial 10-per-column. What's left is 6 3x20 columns and 1 1x20 column. In the last, 4 can be put at most.

cont.

>>9866412
We're at 64. Now for the 3x20s, only about 3x8 is passable (and a single square protruding down from this shape). the theorical maximum of these without restrictions is 13 (3x8/2 + the protruding square)
In this configuration the best shape you can have is a 2x2 square at the top (regardless of what little bitch ben does, in a 2x4 configuration you'll be able to fit 4 stones) and since it's more than 3 away, the same can be done at the bottom, squaring us 8 stones. In the last 4x4 we have 14 slots locked, giving us at most 1 move, for a total of 9 stones per 3x8+lonesquare column, of which there are 6.
for a total of (6*10)+(6*9)+4= 118 moves before Amy's totally fucked for real.

>>9866412
>>9866427
btw are there solutions available or am I going to wait for my gratification/depression pill?

>>9866427

brainlet.

CHESSBOARD.

>>9866943
I missed like 10 spaces because I was counting 6 columns instead of 7 (for x= 1,4,7,10,13,16,19) so the total is 128, not 118
the maximum theoretical amount of non-overlapping knights in a 20x20 chessboard is 140( 7 columns of 20 each or pic related)
If you got other proof to show, show it

>>9867099

Hopeless.

Race war: black v white

>>9865482
I believe the naming terminology goes by Nationality / Ethnic Slur. This is elementary science convention anon, keep up.

>>9865482
Because the US is a proposition nation with no people of its own. Everyone is an American, they simply don't know it yet.

it seems most /sci/entists who are able to solve anything are only able to solve problems 1, 2 and/or 4. Congratulations on your bronze medals/honourable mentions.

>>9867353
What problem you want solved senpai?

>>9867583
>which solution do you want me to copy over from the art of problem solving forums for you senpai?

>>9867353
Anyone has at least a 50% chance of answering question 3 correctly

>>9867619
That warrants you at most 1 point of the full 7. You need to show your work to get points.

>>9867630
>tfw to smart to show your work

solution to #4
100

>>9865542
what a retard

>>9866943
>>9867146
the fuck are you talking 'bout?

>>9865664

Find other qt3.14s here https://www.egmo.org/egmos/egmo7/people/

>>9869698

ai,j with i+j even (or odd).

>>9863785
>>9863792
Chinaman here. We chinks when we think of math are actually thinking of sex. Math is the outlet of our perverted sexual urges because our dicks are too small. We can't even solve something as simple as pic related. The educated and intelligent Westerner probably knows everything and is just laughing at us for being stupid.

>>9862425
Who's shadow bumping this?

>>9865525
The kind of people interested in math competitions aren't the kind of people setting out to become engineers. They're setting out to become mathematicians and the kind of problem solving ability acquired through these competitions is extremely helpful. They also do learn a lot of concepts and techniques which are important to actual Pure Mathematics.

>>9871832
Not really. Since the IMO is so prestigious nowadays people are also using it as a springboard to get into fancy universities.

anti pascal triangle? wtf.. i know how a pascal triangle works but anti pascal? wot

>>9871881
It's defined right there.

>>9871881
m8 they explain how it works right there, it's really simple