Solving the 2006 IMO Problems: Day 1
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- Опубліковано 19 тра 2008
- The 2006 US IMO team members describe the steps they took to solve problems 1-3 of the International Mathematical Olympiad.
Hard Problems is a feature documentary about the extraordinarily gifted students who represented the United States in 2006 at the world's toughest math competition-the International Mathematical Olympiad (IMO).
hardproblemsmovie.com
maa.org
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.
Wtf 💀
Missed call
(1) Harvard
Did anyone else notice that for the first problem, they played a clip of Mr. Feng discussing the SECOND problem (the one with "good sides" and induction)?
Joseph Triceratops I noticed that
@bagula12 I know u?
Yeah
I feel stupid
That's obvious. These guys are ultra pro.
Well you are
You are
Just follow the bijection
Mr. Feng is my Math teacher at PEA!
Wow, all of these guys are getting a PhD at Stanford right now.
Except Yi Sun, who's getting his PhD at MIT.
+probablynotsatanic66 I got a GCE D in English Literature.
+Mike Fuller k
Very nice video, thanks for uploading!
This looks like fun. I wish I was smart enough to participate in the IMO.
Yeah I won all of my high school competitions but those were nothing in comparison to this shit
me too
That requires hardwork bro.
@@kennytheripper2526 no dip, people don’t have time
@@kennytheripper2526talent/gift also plays into factor, however
Am I the only one who noticed that Zuming was describing the second problem first...
excellent.
thank you for this!
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.
@Abel Tatek yes but they didnt choose to enjoy it, they just did. Random.
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!
IMO 2006/1 is one of my first IMO solved.
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.
Phantastic!!!
Oh, WOW, I know Zeb. He's really awesome.
I like what Arnav said about Calculus.
grouch multiplier?
Can anyone explain what that is?
okay i did that first question in the video~ but it literally took me an entire day (._.)
wow you are intelligent broo
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.
Thomas Shadwell ( c.1642 - 1692 )
English Poet and Playwright who was appointed Poet Laureate in 1689.
Awww As a swede i love this, in sweden we argue with our next door country finland over icehockey.
Im moving to asia.
You were at CTY ? Cool. I have a question, do they give you guys IQ tests, or just the SATs.
@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.
Continue please
Oh boy. This debate lasted 2 years.
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.
wow 11 years ago
@@paulatreides9806 wow 11 months ago
NO THEY DONT HAHAHA
Wow 14 years ago
I had Zuming Feng as a teacher at CTY, he was good.
All these guys r at mit and Stanford doing their PHD's
They don't record the olympiad? I can't find any video of them doing these questions in real time.
Well it would be a 4.5 hour video of them taking an exam in silence...
When will we have this available on Netflix or something.
Ey
Haha just realised. Feng is talking about a bijection and good sides that doesn't make sense in problem 1.
This is easy I did it in my head.
@lisinka3 Nevermind, just noticed that the arithmetic progression equality was something he was trying to prove.
lol they screwed up at the start.
Zuming Feng is talking about Problem 2, not Problem 1.
well, that escalated quickly
it's like 3 am starterpack
lol yess
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?
He's saying that we can substitute a=b-x and c=b+y and then prove that x=y. So now the objective is to prove that x=y.
@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.
ye
At 1:18, I didn't know that some of the Hansons is into math!
@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
War & IQ do not correlate at all for a variety of reasons.
1. Constraints imposed by "Rules of War"
Theoretically, the smarter countries would be allowed to use their best weapons (Nuclear, etc) in which case those nations not bright enough to develop nuclear capability would be eliminated. But RoW prevents this
2. Morality (Public sentiment affects morale)
3. Fighters are typically on the left side of the distribution (Darwin corollary)
lol this comment section gold
holyyyy coooww. i have no clue what they are talkin about. wow. i wish i knew math. and use it for something good!! geezz
Yeah sure these guys are smart as hell but imagine the ones that created the problems in the first place
Not necessarily as smart. It is much easier to formulate a difficult problem than to solve one.
@@dekippiesip but after formulating a problem, the person must have an answer to that problem, in order to allow that problem to be used in IMO
@@siddronin8057 yes but they have months to prepare a solution and the internet resources to help them. While the contestants have 4.5 hours and their brains.
Umm btw these problems are proposed by PHDs and other great mathematicians from around the world! They sure are smart!
@@dekippiesip This is so far from the truth it's not even funny. You can make a problem in 2 ways: 1) Modify an existing idea into something interesting. 2) Formulate an interesting problem that might look solvable and try to solve it. Both of these methods require TONS of skill, experience and familiarity with IMO type problems. The set of people that can create IMO problems is MUCH smaller than the set of people that can solve IMO problems.
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.
my brothers
I feel stupid now.
Do you feel physically inept when watching a football game?
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.
WTF! I am glad that I am thick!
@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?
The greatest black man in the world at 4:06
@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.
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.
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.
have they procreated
@Tural192 dude are you serious it's not difficult? they give 4h30min for just 3 questions, i'm sure the problems are difficult
@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
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.
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.
4:02 gril?
Boe
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.
They can be coached for IQ tests LMAO
i wonder what is the purpose of you watching this video?
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.
5:04 .
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
Doubt
Doubt
I worked out in my head that 319 x 58 = 18,502 and that 2,750 x 449 = 1,234,750. Obviously the smaller sum is more difficult!
+Promise Prompri I don't know but whether I can still do them or all the time is very doubtful! I think it is mathematically as clever to calculate 100 x 50 than 319 x 58, as mathematics is simply about the right answer and getting it right! Thanks for the reply, Promise Prompri!
you can do it in parts? --> 319 x 60 - 319 x 2 = 18502
Well said, jip laan! That makes the sum far easier!
Thanks for the reply, Promise Prompri! Knowing the basic times table and adding 0s for bigger numbers helps for calculating numbers in the mind considerably bigger than the 1 - 12 times table.
@KatiushaVN4 I'm a vietnamese but what you wrote here is not nice at all =)
GROSS INEQUALITY:D
Duh.
Too bad, it is not a mistake :P
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.
I Hate math (I´m being sarcastic) (y)
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.
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.
@SlighBaby There are millions others even better than him. There potentials are not being developed.
@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..
Do be stupid.
Lol, why ? The problems they describe can all be solved analytically if you're clever enough
In 2021 I will get a perfect 42 score for India
Shut up
Yessss brooo
Now?
Sooo did u get the 42? Hahah
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?
NERDS !
1:18 i thought he was a girl
4:07 lol a black guy in math competition