Solving the 2006 IMO Problems: Day 1

[MrEagleFalcon]

@lisinka3: That is what he is doing because he says you have to show that y=x so doing that you would have a=b-x and c=b+x

[Dks739]

pee on the circle!!! keep pressing 3

[oildon]

Mr. Feng is my Math teacher at PEA!

[lisinka3]

I got a question. At 5:50 Zach is explaining that you can use a substitution. a = b-x and c=b+y; But if a,b,c are in arithmetic progression, wouldn't it be a=b-x and c=b+x?

[lisinka3]

@lisinka3 Nevermind, just noticed that the arithmetic progression equality was something he was trying to prove.

[NinjaXSong]

@openuniverse2003: I'm curious to know how you live your daily life, and what job you have right now (if you even have one)

[zadeh79]

The only one I can get right is number 2 (and this is within about an hour or so) But I'm 32 years old, and a University graduate. Wow these kids are smart!

[rinwhr]

4:07 lol a black guy in math competition

[777kamasutra]

@rinwhr racist mother fucker!

[openuniverse2003]

@rinwhr Not "lol", son, but "LULZ"! 

[FairyMeme93]

@SettoRyokuH3 : there is 14 years old and younger in peru team , go check .. !

[SettoRyokuH3]

right now im just an average teen...14 to be exact. Give me 3years and i will be in the IMO.

[enlaorilladelmar]

@SettoRyokuH3 that is the attitude ^^!

[MrDebashishMohanty]

At 1:18, I didn't know that some of the Hansons is into math!

[juniormooNo]

wow! 

[Abdullah2009]

GROSS INEQUALITY:D

[bass109]

Jesus is coming soon! repent and prepare for the lord

[Creolebway]

holyyyy coooww. i have no clue what they are talkin about. wow. i wish i knew math. and use it for something good!! geezz

[tetrissuckit]

If you guys want to prepare for olympiads, there are lots of resources for competition math at Art of Problem Solving

[jvboy88]

they are god gifted, which i cant be jealous of though i wish i was gifted like them then life would be amazing for me.

[Tural192]

Problems arent so difficult.The main reason for this that this guys are trained by strong teachers.May be they have done problems which is 80 or 90 percent similar to this problems.

[sedmoagalnikful]

@Tural192 precisely , u just have to get the best teacher , to show you the method , the idea , then its just solving

[btkw]

@Tural192 dude are you serious it's not difficult? they give 4h30min for just 3 questions, i'm sure the problems are difficult

[Tural192]

@btkw, problems are difficult but not so...i mean that...problems like these you can find in county math olimpiads...

[Fand421]

what the heck...take your quarrels someplace else. this video is about math!

[Vietnameseboy1993han]

@Chinastar85 I know too much annoying Chinese around here , to write it here.

1)Chinese dont like Viets (dont need to explain)

2)Southern China was origin Vietnams. Have you ever see the Zhou Dynasty ?Its long ago , but China would like also to take their own land back.

3)China want to destroy Vietnam and take over us.

4)Chinese want and have sabotage my country and still.

5) Im from Norht Vietnam and I wont let you guys do what you want , ok ?!?!

[jeff1011011]

I love problem solving. I got a late start at it since I come from a country where it is not emphasized at all but there's something fun about solving problems. A huge part of problem solving is experience with and exposure to problems, and knowledge of how to approach them. Some problems require what might be termed "extraordinary insight", but the solutions are rarely complex. It's just a matter of seeing the problem for what it is.

[Vietnameseboy1993han]

@Chinastar85 No other way. You chinese make us viets care a lot more about ethnicity. especially youre racis against viets with youre friends.

[Vietnameseboy1993han]

@Chinastar85 you and youre chinese friends care A LOT of ethnicity. so typicall...

[s900203]

Agreed. Hard work can get anyone higher in any field. But IMO is just different... Especially to qualify for it in the States requires a lot of natural gift.

[amesakurako1]

okay i did that first question in the video~ but it literally took me an entire day (._.)

[spondulas]

I wish I was a genius...

[SlighBaby]

The greatest black man in the world at 4:06

[bodwisa]

@SlighBaby There are millions others even better than him. There potentials are not being developed.

[SavetheStarving]

they arent genius' they are just really smart and focused

[mozart20dlubos]

@SavetheStarving No. They are geniuses

[angela1894]

The indian dude is Arnav Tripathy, and he has won the Putnam competition 3 times, he should win it again this december, which would make him one of very few 4-time winners.

[buker420]

these kids obviously use a massive percentage of their brain compared to the normal human being, fuck this is awesome!

[PowerFromAbove]

I wonder if any of these kids will ever see a vagina?

[TheKiimii]

@PowerFromAbove you're such a noob. Is their choice whether to marry or not.

Also, if there wouldn't be ever such geniuses, the world wouldn't be what it is right now.

[glutamin111]

i wonder what is the purpose of you watching this video?

[bleucheese14]

Do be stupid.

[HoSayLiaoLah]

@PowerFromAbove

I am sure they would prefer to see a mathmatical equation than to see a vagina.

[dmanc1]

@HoSayLiaoLah lol

[jwang059]

And before anyone start saying things on the lines of China always beat other countries due to a higher population, keep in mind that over half of China's population is rural and receives poor education(rare chance of IMO candidates here), and China has the one child policy, yet China trashes every other country. Similarly, small Asian countries such as Korea do far better at the IMO than European countries with similar population.

[HowAboutSomeTruth1]

@jwang059

Jews usually win at these things, in terms of "population:genius" ratio.

[jwang059]

People who think IQ is of any significant importance should think again. What makes you think Certain countries ALWAYS does better then other countries at IMO? Are you possibly suggesting that some nationalities are far more intelligent than others?

The difference between an intelligent person and a genius is trivial, it's the work they put in that sets them apart. Like someone said earlier, intelligence is akin to velocity and work time, while success is displacement.

[jwang059]

Lol... I like how some of you actually think IQ tests are a good measure of intelligence, and somehow genetic advantages is more praiseworthy and somehow superior than hard work.

there is a Chinese-american mathematicisn who won the fields medal in his 20s and he only has an IQ of about 130.

[thewiffenpoof]

The youngest to win the fields medal was 32 or 33 when he won it. That was Terry Tao who is not Chinese American but Chinese Australian. He has an estimated childhood IQ of 200 to 230 according to his bio on an australian newspaper.

[KatiushaVN4]

As for Canada, LOL we Asian (Vietnam, China, Japan, Korea) are far above you in number of GOLD medals

[hvutrong]

@KatiushaVN4 I'm a vietnamese but what you wrote here is not nice at all =)

[556pilot]

@hvutrong yes... she acts like that and it makes vietnamese people look bad. but i know that not all are like her, ive met many more that are nice people :)... she is not nice at all, and not a person that represents vietnam

[KatiushaVN4]

My source is: IMO(dash)official(dot)o r g

[YSFmemories]

If we look at the past ten years, the number of perfect papers, or the number of golds, China trumps Viet nam by a long shot.

[rosenberg011]

@YSFmemories I realize you commented on this a while ago but this is intended for your comments about Vietnam and mathematics: Kind of funny that Ngo Bao Chau won the Fields medal isn't it? Btw i am not even Asian I'm Egyptian so don't take it personally :)

[YSFmemories]

@rosenberg011 Hi, I'm sorry if you read my comment the wrong way: I never meant that Vietnamese people are bad at math!

It's just that China has a much larger population than Viet Nam, and cares about such competitions a lot more, and has special classes for them since elementary school. Obviously China would do a lot better, unless the Vietnamese are a LOT smarter than the Chinese, which I doubt.

I'm not saying the Chinese are smarter than the Vietnamese though.

[rosenberg011]

@YSFmemories I didn't say you said the Chinese are smarter than the Vietnamese. You said in a post that the Chinese are historically better overall at Math. Look I'm not here to argue. Like I said I am Egyptian.

[YSFmemories]

@rosenberg011 Oh, but it doesn't matter whether you're martian or plutonian. I don't look at people by countries, especially one as rediculous as Chinese vs Vietnamese, when the peoples of the two countries are so similar.

An argument isn't always a bad thing, you know. It stimulates the brain, and causes you to think. It's not like I'm flaming you.

I never said that the Chinese are better at math than the Vietnamese. I'm saying that because there're more Chinese people

[rosenberg011]

@YSFmemories Hahaha your point about argument is true but only about meaningful arguments not something so trivial and subjective.

No that was not exactly what you said but that's what I understood from what you said. Like you sort of mentioned, I believe that one's country is irrelevant to his/her mathematics (or anything for that matter) potential. Thanks for giving your time to clear that up.

[YSFmemories]

@rosenberg011 there are bound to be more people who are good at math.

If I said the exact words "the Chinese are historically better overall at Math", I'm sorry. That's not what I meant. I meant that because there are more people, there are more people that are good at math. There are also more that are bad at math. Make sense?

[KatiushaVN4]

Vietnam = number 1 at Maths in Asia

[YSFmemories]

lolol? Go look at the rankings, buddy. China and japan are always ahead. Mostly china, though.

and quagmire: Isn't that exactly what i said?

[KatiushaVN4]

YSFmemories:

Vietnam is the current country in Asia that earns most of the medals at IMO with 183 medals in total meanwhile China 138 medals and Japan 111 medals. I'm talking about the TOTAL medals (from the past until now) including gold, silver, and bronze

[YSFmemories]

Will you share your source? I find that unbelieveable. Unless vietnam joined the IMO long before China, I don't see how that's possible.

Furthermore, I don't think you can say that having "the most medals" count as being the best in math.

1. Gold medals are much more impressive than silver, which is still moreso than bronze. To weigh them the same is rediculous.

2. A highschool math competition doesn't make you good at math.

[KatiushaVN4]

Oh yeah?? Don't you Canadian and American count only the number of medals?? For example, in Beijing Olympics 2008, you guys only counts numbers of medals to rank countries' places regardless of gold medals...

[YSFmemories]

It's good for propaganda, obviously, as China dominated the gold medal count.

It's not as if I agreed with it... In fact, I detest western media.

Anyway, 2 wrongs don't make a right. Also, I'm still waiting for a source. Thanks. it's not that I don't trust you, I just find it amazing. And I want to see other countries as well.

[KatiushaVN4]

w w w (dot) imo (dash) official (dot) o r g

[mikolandon]

In IMO what determines the places for each country is the sum of the points of the contestants.

[ihateuutube]

You're a moron. That's because Vietnam has been to far more IMO's. China only started participating in IMO in the early 90s. Since then, they have dominated the event and won pretty much every year. China's team has gotten all golds 9 times. No other country has done this more than once.

[KatiushaVN4]

@ihateuutube

Shut up! China has participated IMO since 1985, not early 90s you dumbass.

Not to mention China has the population 17x Vietnam's population

[nuketothesky]

@KatiushaVN4

China always get 6 gold medals, you know what? It means there might be more than 100000+ Chinese students might get gold medals. There is nothing shame to have a low IQ man, take it easy.

[KatiushaVN4]

@nuketothesky

Vietnam currently has most of the medals in IMO. So stop making excuse! Vietnam is the second Asian country that wins Field Medal. So who is more stupid than who?? Heheh Then stop crying. OK?

[nuketothesky]

@KatiushaVN4

'International_Mathematical_Ol­ympiad'

'IQ_and_Global_Inequality'

please read these 2 articles on Wikipedia carefuly. before making conclude, you should always either do research by your self or at least look at some reference first. This is how we work in University (a good one, not like the pheonix university of the US).

[KatiushaVN4]

@nuketothesky

Stop crying about that stupid IQ already. No-one gives a damn about it. If you post Wikipedia as cited source in you paper in university, I guarantee that you shall get an "F" for your essay. Stupid ass

[nuketothesky]

@KatiushaVN4

Wiki is only used when debating with you, If I post the article from the IMO official website or from the author themselves that's a long story and that's difficult for you to understand I supposed, If you want you can look at them. Doing research in University of course based on real materials and good reference.

[KatiushaVN4]

@nuketothesky

Well, I didn't mean to offend you about education. I want to take my previous words back

[youtert]

I had Zuming Feng as a teacher at CTY, he was good.

[angela1894]

You were at CTY ? Cool. I have a question, do they give you guys IQ tests, or just the SATs.

[youtert]

The Young Students program (5th & 6th grade) used the PLUS test which was an SAT-style test, maybe similar to the PSAT. The older students just took the SATs.

[angela1894]

I hate that they've phased out IQ tests. IQ I guess is no longer a PC concept. I really feel that SAT tests can be learned, and are not a true measure of intelligence. Kids can be coached to do well on the SATs, but can't be coached to do well on IQ tests.

[angela1894]

I believe these kids who do well on these math olympiads might be the smartest people on earth. I know IQ tests are more than just math, but I am sure that anyone that can do well on these math olympiads will have no problems acing an IQ test. All these kids in this video have at least an IQ of 180.

[YSFmemories]

There are only so many people with 180 IQ in the world. 140? I agree. 160? Probably a few of them are pushing it.

But it's important to note that they get in the IMO not by intelligence, but by hard work. Having done math contests myself, I know the amount of work needed.

I consider myself to be quite smart. Without studying, I can get maybe 2-3 on the AIME. That's it. But then if I want to improve to 4-5, the amount of work needed grows exponentally.

[angela1894]

IMO is also about intelligence. Yes, it does require hard work, but it also requires a solid background of intelligence. Without the intelligence, no amount of hard work will make you do well on the test. And your hard work will boost your scores only to the extent of your intelligence

[YSFmemories]

I don't believe so. Intelligence is merely the velocity whereas knowledge is the distance.

Anyone can solve IMO given enough work. It just takes some people longer than others.

but i do agree SAT has nothing to do with IQ. I mean the math section is freaking easy, and English had nothing to do with IQ at all. It's an irrational, illogical man made language... and the vocab is just memorization.

[mikolandon]

i got silver medal in 2006 and i never did above 150 in a IQ test.. ive done a lot

[angela1894]

@mikolandon You never did above 150 on an IQ test because you most likely took the Weschler IQ test which has a ceiling of 150. This implies that your IQ is most likely far above 150, i.e. 150+, too bad your school did not pick up on this.

I'd guess your true IQ is above the 180 range, because being good enough at Math to get a silver medal on IMO implies you have very superior analytical skills. Thus if you had taken a higher-ceiling test like Raven's Matrices, your true IQ would emerge..

[zadeh79]

@angela1894 The Raven's requires fluid intelligence more-so than crystallized intelligence. Although IMO problems have (hypothetically) unknown algorithms, and thus qualify as true 'problems' (unlike items on conventional tests of intelligence) , their properties of abstraction are not unusually high. They require a lot of knowledge, and lot of crystallized intelligence, including pure analytical thought, but 'moderately high' in terms of abstraction.

[zadeh79]

@zadeh79 A good example of a math test which progresses towards problems of extremely high properties of abstraction, and is a better measure of fluid intelligence for those with a math background, would be SIGMA test. It is free to take online, and has no general time limit (I'd say to give yourself a couple days). The SIGMA undoubtedly requires a fair amount of crystallized intelligence, but the fluid properties increase as you go through the test.

[quagmire444]

ok an IQ of 180 is so rare. yes there are people in the world who have an IQ that high but it is rare. having a hi IQ helps a lot but studying hard and working can be a great assistant.

[gnihtyrevEnoitseuQ]

I'm curious. For problem 3, Zeb says that it's not a symmetric inequality, but a cyclic inequality, and becomes symmetric after squaring both sides. Why then does the official proof say the inequality is symmetric after the factorization? The solution says

"... |(b − c)(a − b)(a − c)(a + b + c)| ≤ M · (a^2 + b^2 + c^2)^2. (1)

Note that this expression is symmetric, and we can therefore assume a ≤ b ≤ c without loss of generality."

Is there something I'm missing?

[bordway]

lol funny kids.. wouldnt suggest them a numerical methods course

[angela1894]

Lol, why ? The problems they describe can all be solved analytically if you're clever enough

[ravenxclaw]

4:01; cute girl. :D

[hoodloom22]

You know what's interesting to me is that so many people attribute math ability to pure talent but some of the greatest minds like Newton and Gauss simply had the ability to focus hard for long periods of time. Even Gauss said, "Whoever thinks as long and as continuously about mathematics as I do, will make my discoveries. Now, it is very possible he had amazing natural talent, but it also shows his grit and mentality.

[ihateuutube]

Genius people tend to say things like that but that doesn't mean they weren't exceptionally intelligent. Gauss in particular had a mind that any objective observer would call "pure talent". He was human calculator with an eidetic memory who could conceive of things no other mind could.

[dmanc1]

@ihateuutube Look at the Bernoulli family.

[openuniverse2003]

@hoodloom22 Newton died a virgin, and Gauss was WEIRD. People who are THAT smart should at leaast be able to get a hooker, no?

[thisismymoniker]

It sounds as though the team coach Zuming Feng from 0:27 to 1:17 is talking about problem 2 rather than from context problem 1...he is talking about 'good sides', bijections and induction. Surely the documentary makers can't have edited the comment into the wrong question...and if they did, surely it would have been corrected on checking? Confused!

[MalaTemporaCurrunt]

@thisismymoniker

you are right. they surely did non check.

[goodluckpeace44]

long live those people

good luck!

[axlemn]

Oh, WOW, I know Zeb. He's really awesome.

I like what Arnav said about Calculus.

[FriedCheese123]

I know this got quite a bit of negative feedback, but as someone who actually does this sort of math, I can testify the truth of this statement. Indeed, being an actual genius at math would set you apart from others, but immense amounts of hard work, no matter how intellectually capable you are, is generally sufficient to place you among the top.

[goodluckpeace44]

thats not quite it. mathematics is talent. sometimes you get lucky, or you are having some extraordinary talent of intitution, but I think that peple in this Mathematics olympiad and first order mathematicians had a natural talent in the subject. There are people with just one theory that is when you work hard, there are people with 100 theories, or more that is by natural talent I say

[MelkorNoir]

You spelled genius wrong.

Hence your long winded argument is invalid.

[GeniusJohn16]

Any one knows where I can watch this movie for free???? Please and thank you =0

[Khemix4]

excellent.

thank you for this!

[iconjack]

Yeah, I watched the problem description in the first minute and then paused to get a little bit of a grip on it before proceeding. When I resumed, Mr. Feng was talking about solving by either finding a nice bijection, or using induction. I couldn't even imagine what you'd induct on to solve this geometry problem. An editing mistake, I surely hope.

[Abdullah2009]

Too bad, it is not a mistake :P

[damagejackal10]

Phantastic!!!

[lighangel]

grouch multiplier?

Can anyone explain what that is?

[notreallyanfa]

Lagrange murderplier - er, multiplier. Look it up on Wikipedia or something. It's a powerful technique for solving inequalities using calculus.

[AsianShoey]

Lagrange multiplier*

It's contrained optimization, you want to max/min some function, with some contraints. You need to know a fair bit of multivariable calculus though

[ihateuutube]

whoa, wait a sec. is this the final version of the movie? From 0:25-1:20, Zuming Feng is definitely talking about Problem 2 even though it is supposed to be about Problem 1. Looks like someone messed up editing there.

[kurtloderlovespie]

bitch no ya aint

[lamfsc]

ABsolutely FANTASTIC. THANKS a lot.

[zashley43]

Awesome!!!

[cookyjoan]

awesome

[v123sl]

awesome video

[zsyed12345678]

Thanks for posting.

[TubeGuest5178]

AWESOME!