I tried the Harvard-MIT Math Tournament but I can't even
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- čas přidán 6. 06. 2024
- Watch full solutions to Q7 and Q10 by @pkmath12345: • Solving a Challenging ...
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HMMT past papers and solutions:
www.hmmt.org/www/archive/prob...
2021 November: www.hmmt.org/www/archive/251
2021 February(March): www.hmmt.org/www/archive/242
HMMT Website: www.hmmt.org/
HMMT Wikipedia: en.wikipedia.org/wiki/HMMT
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Timestamps:
0:00 - Intro
1:06 - Nov 2021 General round
7:12 - Nov 2021 Theme round
8:09 - Nov 2021 Guts round
9:21 - Spring Tournament
11:10 - Past winners
12:43 - Patron Cat of the Day - Věda a technologie
Wow! Great video as always Tibees! I appreciate you introducing other sections of HMMT exams with your great work and also it was my honor that my videos are introduced in your video! It was great working with you at this time! Hope to work together soon :)
I watch your videos too tor mu jete prep indian😌😌thank god my concepts are cleat
@@promitaghosh4027 Thank you sir haha👍👍👍
@@pkmath12345 I am indiaan I watch your video
@@alokkumaryadav6209 Thank you very much sir haha👍👍👍
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Every time I feel like I am decent at Math these tests humble me down.
same lol
me too :(
+1
Hell yeah dude:(
You can be very good at math and not good at these questions.
hey! i'm the "Sean Li" author that wrote a lot of the problems you presented (including nov general #1, 2, 7, 10). glad you enjoyed the problems! big fan of your videos and feels a little funny that i'm in this one :')
On the first General Round problem, the answer I found was from visualization.
1. Starting with red, simply place the solid red domino between the other two red ends. This is our first position and counts as 1.
2. Remove the solid red, slide the two end pieces together.
This is our second position and counts as 2.
3. Mimic answer #1 using the color blue.
This is our third position and counts as 3.
4. Remove the solid blue domino, slide the two end pieces together.
This is our fourth position and counts as 4.
Forget using *only* ABBA logical constructs.
Math works better when supplemented with visualization.
I had a go at q2, very nice!
You look like you're 10
What were you on when you thought of questions 7 and 10?💀…jk but good job with the questions!
Answer to question 7: Why does the answer not mention that you used (a-b)*(a+b) = a² - b² to get f(x)?
Also it is NOT comprehensible how you get f(t) = x!
Is it too much effort to present a FULL answer?
I have a Ph.D in Aerospace engineering, I always considered myself excellent in the higher level math, and I can do a few of these problems but I would fail miserably if I had to take that test for entrance
You'd do well if you had a week or two to prepare intensively and knew what topics were coming. Hard to just do these out of the blue.
Because these are just math riddles made up to be difficult to solve. I'm not sure if professional mathematician would solve all them if he never tried before
Well, good thing it's not an entrance exam!
Aerospace engineering is a specific skillset, just like advanced mathematics is a special skillset, just like solving these math riddles is a specific skillset.
You, without any doubts, need a very high IQ to be able to solve these fast, but it's still just a specific skill which people who are able to solve these problems trained for decades.
@@jaroslavprucha9198 can't be formulated better
I bet I could study hard enough to eventually understand some of those questions but I can’t even
You can't even what?
@@LuceroAlvarado I just can’t even
@@sullyster6738 totally understand. I can't even as well.
@@javipena93 I can't odd
I guess I'm different ...
@@LuceroAlvarado sorry I can't be your man
3:21 😂😂
One hour ago?
You are here really ? Can't believe
Yes nice 😂
Hey bprp, love your videos. Why don't you upload solutions to the weekly HMMT problems? I find them quite challenging and interesting
this clip is oddly funnier at 0.5x speed
Fascinating math test! Thanks Toby.
I suppose the trick with these type of questions is that you have done a lot of similar types of questions and you already half know the answer.
I know these people are mega smart but they are also incredibly hard working and if you never done those kind of questions I think you would truly be a genius to answer them really fast.
Hard work and practicing is so important for doing well in mathematics. This seems often overlooked.
you just described math. Most poeple that are good at math and fast doing this problems have already done similar problems. If it's your first time you allways take way more time.
@@paulogaspar8295 Yes, but HMMT's problems do not often take a similar form as problems before them, especially recently... So these people definitely have a lot of analytical skills
Yeah dude I can do these questions in like an hour or so with a bunch of head-scratches and retries with different approaches, so clearly if I practice it enough I should be able to do them under 15 minutes generally. These competitions aren't much for the gifted tbh, they're for those truly passionate about math.
@@arinroday302 he said "done alot of similar question". He didnt say anything about the question being repetitive from last competition or anything. In math, if u do alot of exercise, u tend to encounter similar one. That's why he say "half the answer".
So repetitive to what???
Great to hear from you again! Hope all is well girl!
Thanks Toby for the new great episode. And self talk part was really hilarious ))
I'll be honest with you, All this goes way over my head but i cant stop watching simply because i love to hear Tibees voice.
Exactly. I would have liked her to be MY teacher.
She is of the few people who have a natural asmr voice
Thanks a lot! Especially for researching about past winners and presenting some of their current careers here. I hope this really encourages future Math (or any other subject) aspirants.
"A knight attacks another knight if the distance between the centers of their cells is exactly √5"! So good.
I wonder how many chess players think of it like that?
@@vk2ig They're playing out sequences of moves and if their position will be better at the end and they fail to realise the checkmate in 1 that's one in the middle of the board
HEMA practitioner: "Well, depends if they are using polearms, arming swords, two handed swords, war flails, bows, maces, pikes, axes?"
r/unexpectedfactorial
@@arinroday302 Abacus error #457: unable to compute factorial of ' √5" '.
Tibees, you're a great teacher. You translate hard to understand concepts and actually make them as understandable as they can be. Thank you.
Great! Can't wait for the English version.
This would give my math teacher nightmares 💀
-literally=same meaning
@@mavfan1 yeah true
How cool. Thank you for introduce us to the beautiful universe of HMIT math!! cheers!
Love it. Thanks for being so honest about not understanding. These tests are intimidating even for those of us who have done some advanced math.
This video certainly brings me back! I competed for Lexington in the main tournament in '07-'10 (and also in '05). Our teams did pretty well most of those years, with several of us breaking the top 10 on the individual rounds and the teams often doing likewise on the team and guts rounds, though as a public school we were always overshadowed in the overall standings by the magnet schools.
I always loved the guts rounds in particular. There were always strategic meta-questions such as how much time we wanted to spend trying to confirm our answers on a set, or whether we wanted to punt on a question to advance to the next set, etc. The last set almost always had psychological questions where your score potentially depended on everyone else's answers. Part of the excitement was also that the sets were graded in near real time, and the running scores are displayed live during the round. It was a certainly unique format among the more traditional high school meets and olympiads, one we pretty much copied when our HS launched a similar middle school competition.
Loved your spirit and thanks for inspiration ♥️♥️
Thankyou tibees for this charming description of a difficult preoccupation.
I remember meeting Luke once back in middle school in MATHCOUNTS nationals (my state coach knew his state coach well) and he was just insane, got 2nd place nationally in 6th grade and 1st place in 7th and 8th (he's one year below me), not even surprised when he won the one time I participated in this competition
Orz
I went to nats in 2019 lol
It's way too late to learn this level of math but I find it very relaxing to hear about it. Thank you for all of your effort.
When is too late?
@@wafflewaffle8529 when you work on a full-time job and don't have a youth anymore where you could invest your time almost in anything
@@johnnya1717 oh :( , if you really want something though you …
@@johnnya1717 Instead you just invest part of your time. 🙂. Don't give up so easily!
@@wafflewaffle8529 For me it's now. My health is poor and I spend what time I have left trying to organize things and reduce what possessions I've accumulated to make it easier on my family.
Got to go with a team to this once in February 2020, it was the coldest weekend in Massachusetts when the competition was held (single digit in Farenheit) and I was happy to just get 5 questions correct on one of the sections. Guts round was kinda fun though but of course my team wasn't gonna win anything there either
That is a very great concern of you. Well, detailed mentioning.
Yeah, question 7 caught my eye too. Woof, that's nuts; don't know what more to say. Well, thanks for the survey of these!!!
I'm so happy you mentioned Ricky! He is from the high school I teach BC Calculus and am the Math Team Advisor. Unfortunately, he took BC in 8th grade before I got there. He also participated in the IMO. I practice Putnam and IMO problems with some of our top mathletes or just for fun!
good to see someone from NZ and talking about MATH!
I was so worried because of no uploads. Thanks tibees❤🌹
Thanks for this info
This was way over my head, but I listened to the whole video because I like Tibees voice!
At 3:05 the different form for f(x) is simply multiplying something of the form (a+b) by (a-b), which was done on the top and bottom of fraction. This allows you to set up a quadratic equation to find x (I am guessing since I went straight down to the comments) with f(x)=1. You'd then sum the solutions from this. The answer, with the square root, looks like the quadratic equation too so this can help you realize this.
Very good work toby. Thankyou. You brought in your contact PK.
It doesn't really look that bad honestly, these actually remind me back in my high school days doing those kind of math questions to train our way through competition and to IMO. I think the hardest part is to keep up with the time limit though, cuz i don't think i can do 10 of these in just 50 minutes, even back when i still had it in me to do these kind of silly questions that don't help me nothing now.
Do you think doing competition math has helped you later in life?
Don’t worry Toby, I believe in you. Wow! Some of those questions can fry a few brain cells. I was expecting a video from you on pi day. Anyway, this one is great. A little question: Wound you be going into production for plush ‘X’ type toy from your treasured Finding X video? May you stay in good health.
American π day due to their way of writing dates. 😁 ... Bye, bye, American π ...
We can't have π day in countries not using that date notation as there isn't a 31st of April.
I realy enjoy your video thank you
i just watch ur videos for ur voice ..total asmr for me
Wow! This video is full of graphical explanation and memes. Thanks for making it study with fun.
Have you seen 3Blue1Brown?
Watching your video makes me interested in math :)
I participated in the tournament before. It was a great experience.
hahaha I really loved your camera effect for the "I can't even" segment at 3:30
I’m lost. But, with your voice guiding me, I’m happy about it.
Her voice is sooo relaxing. I need to listen to her talk while I'm driving around in traffic here in D.C.
The "let n be the answer to this problem" ones are really cool. For example, for #2, if there are n white balls and m black balls, the probability that the first ball is white and the second ball is black, is n/(m+n) * m/(m+n-1), but it also equals n/100, since n is the answer in percent. Set these equal to each other and rearrange to get (m+n)(m+n-1) = 100m, so the product of two consecutive integers has to be divisible by 100. It could be 25*24 = 600 or 76*75 = 5700, either of which gives n = 19.
I think that they only seem "cooler" because they're generally easier to understand, therefore you feel more capable when approaching and solving the problem (my opinion, at least)
I can solve them all, however not in 50 minutes, but in 50 years.
I sat these exams! Competition math is its own genre of math and requires special preparation. The vast majority of people score at most 4 out of 10 on the February individual rounds.
Yup!
And those scores are enough to place you as remarkably unfathomable when placed among a regular group of people! Hahaha
Interesting video article. Real time competition you are describing ,I thought was in the same vein as the "Times" newspaper crossword competion
I became discouraged when I saw there were no questions with multiple choice answers.
This really scared me and made me think about my future plans.
I do think that for one to ace the questions, hard work will be required,I mean,they only seem difficult for the one who has not studied about them, but once one dedicates their time to working on the questions and unlocking the tricks,then it'll no longer feel like unfamiliar territory.
Absolutely agreed
While the contest is hard, if you do very well multiple times (top 10) you're almost guaranteed acceptance at top universities.
The people who do well in this competition are not caught up with going to the top universities.... The prestige of top universities impress laypeople more than those who are educated, especially those who may eventually become the top of their fields.
@@jonathanyang1423 ok Jonathan
I read the title and knew that this was gonna be funny. I went to HMMT once and it was a blast but the problems sure were difficult. Didn't really solve much of anything.
Tibees showing the Mr. Krabs meme at the easiest part of the question. Well not that I blame her, that ending part always looks way harder than it actually is :p
I'm a freshmen in highschool, and I've been competing since 4th grade. It takes a lot of dedication to do good; I trained 6 hours a day for several months prior to the exam to come 24th.
Impressive!!!
Was there anyone younger than you ahead of you?
@@mustaphad1319 Yes, lol, there was a 4th grader from Texas who was on the winning team, he got like 7th individual. Most people were around my age.
Based on the 10 exams I encountered for my MSCS degree, these appear to be Math PhD exam questions. Possibly entrance exam questions. Someone I know who passed the CompSci PhD entrance exam did so while working a job and not taking courses and likely used most of his vacation days to study for the exams.
grad school maths would be a lot more theorem heavy i reckon, these questions are hard but most of them can be solved with a bit of exploration and ingenuity. some of them have a "trick" which once you see it, the whole thing appears obvious. grad school maths is like trying to read an alien rune language of weird notation, boring or wacky names (spectral? magma? ring? field?) and surnames of people
i dont think so, these questions are based on the high school curriculum but twisted in a very clever way.
@@gasun1274 Cheat sheets are a sign of stupidity, not intelligence.
Nah we do them a lot in the Associate CPGE
@@ndotl no
I understood the words you were saying but I did not understand what you were saying...hahah great vids thanks.
I upvoted after finishing chuckling over the "I just can't" segment.
The filter at 3:20 definitely goes over my face when reading hard math.
great video :D
Im glad to know as a high school freshman I can do half in the 50 min timeframe. Some pretty impressive guys on the winners list. Thanks for the video!
Teach me bro
subscribe to Michael Penn and letsthinkcritically, watch like 5 videos a day and try to do each problem for 30 minutes before watching the video. Repeat this for a year and tada, you can solve these problems! Most of them are very similar and you just need to master a few techniques.
@@hilbertonfields Well actually you see I am an 8th grader going to be 9th grader by 4 April and I really messed up learning maths chapters like- I did exponents, logarithm, trigonometry, calculus...(in that order)
I need to do many things before this I guess
Thank you for your answer though
Impressive!
The thing about these math tournaments is that they're more about parlour tricks and trivia. Almost no one is reasoning through them front-to-back in any deep way, but instead are using niche methods that they've already picked up.
Keep me in your Team Toby, With people such as you and Dr PK Math We can show our mathematical muscle with these tournaments !
THIS VIDEO IS A NIGHTMARE FUEL. 😭
And there will always be that person that calmly turns their paper in after 20 mins, getting all the answers correct and points out an error in one the questions to the professor who has to concede the point and makes the rest of the students aware of it.
Question 1 does not specify the number of dominoes used in the arrangement, therefore the correct answer is 16. The answer is only 4 if the number of dominoes in the arrangement is exactly 4. This constraint was not specified in the problem.
Number 7 looks very interessting. BTW I just finished my phd thesis in algebraic geometry. But I have no idea how to tackle some of these problems. People train for such tests, like runners do when running a marathon. Having an IQ of +160 might also help, but dont underestimate the power of traning :) I think this test does also serve as a screening for students that might deserve some special attention. An easier test wouldnt be meaningful enough for that matter.
Congrats. I finished my PhD in topological algebra in '92. Time flies. How's the job market?
@@barneyronnie I finished my masters degree nearly 8 years ago. At that time there was no job for a phd student available (at least not 1. where I lived and 2. where there was a professor working in my field of research). So I started working in the reinsurance business. After over a year my former master thesis advisor contacted me. He finally got a full professorship at a well known uni. But I already had a real job. So I did my thesis for fun, while working full time as an actuary and spending my vacation at the uni in seminars and talks. It took me 6 years haha. The defense will be in early spring. So there is no problem finding a job. I already have one ^ ^
I can’t even do basic math, I’m a human failure
So am I brother, so am I.
Me 2 😂
grind
If you think that you're a failure due to your lack of understanding of a subject, then school did its job. On a more serious yet optimistic note, it's never too late to practice!
@@jacobschiller4486 Maybe school did its job?
Or maybe their parents did their job, and/or their peers inside and outside school did their job, and/or the school bully did their job, and/or the little country town they live in did its job, and/or the wider society in which they live did its job ... etc, etc, etc?
There are many reasons why kids are "put off" mathematics, and the school system is just one part of the problem.
Have you ever seen entrance exams for Polytechnique or ENS (Ecole normal superieur)? You should definitely have a look on it.
eh oui la France les goatss (jdeconne notre niveau s'effondre lol)
I saw a couple videos from Mathcounts competition where Luke was doing really well at since like 7th grade
how do you smile and speak so naturally about math
I only looked at the first set of questions for any length of time. The first two I could do in my head. Question 3 I got 807 and Question 8 I got 247, but I haven't checked the answers yet.
That made my brain hurt. LOL! Seriously, I don't think even at my peak I could've solved very many of these...
You made my nose bleed from reading question 7. I'll watch the rest of the video when I feel much better.
3:22 Might be that high school exams evolved and they learn this nowadays already in high school? Every year it says: "Things have been fundamentally revised in order to meet the new challenges of the new upper school and the new curriculum." So they constantly work on new things to upgrade math at schools.
@Tiffany Wart might have been when you made your high school exam. But things are changing every year. Math school books are changing every year. Curricula are revised almost every year .
i won a year(maybe semester)-long monthly math thing while attending uni. the math dept posted one math problem a month to solve. i solved the most (idr if i tied w/ anyone) and got a bag of goodies at the end and a certificate lol oh and they were not as hard as the HMMT problems lol
For question number 7, you get that expression by simply multiplying the numerator and denominator by (x^2 - sqrt(x^4 + 2x)) and use the every so ubiquitous equality (a + b)(a - b) = (a^2 - b^2). The rest, well, I haven't any clue.
Who ever is solving all is super gifted.
No they aren't. You just need to work hard to reach that level
@@siddharthnair961 and money 💀
@@rim_des7652 Exactly
Actually, it takes effort
I like how the 2008 winner streams on twitch now
Who is it
The trick at 3:04 is such a nice one, but omg. To get to that version of f(x) just multiply both the numerator and denominator by (x^2-sqrt(x^4+2x)) and then everything falls into place. LOOORD I love this :D
Ohhh... I didn't see that.
I'm consoled by the fact that after all that indepth math you still showed some regular stalking skills at the end of the video.
"i just can't even..." got me forwarding this video to my daughter.
Yeah Tibees... I'm with you. I can't. I just can't. And these are 17 year old kids that are solving these??? Geez, it actually gives me hope for the next generations coming up.
In a population of millions a few are statistically bound to have this level of intelligence. I met a few of them in university, one who won the Dutch physics olympiad, another in the top 10 of both the physics and math olympiad.
They operate on a completely different level. Whatever is explained in class is understood immediately at run time without any effort. If I think I am intelligent I need to think again.
A lot of students that can solve these don’t even get to take this competition.
Please try the questions of the International Physicists' Tournament
#2 looks brutal to me. Like Goldbach's conjecture or something.
Liked the presentation. The first question's answer might be to assume that all tiles are individual or unique, regardless of the tile's color scheme. You went past the several questions in the middle pretty fast. The last question, more time was spent, and there are 3 related equations and 3 variables. Solve for the three variables, using the equations, and then substitute. Some pencil work for this last one, but there you go. Much of math, or even life, it seems, depends on your point of view.
HOLY SHIT I WAS ABLE TO SOLVE ONE OF THE THEME PROBLEMS I FEEL SO POG RN
I appreciate the first one being a gimme so much
How do the jury make the problems in the first place? Do they find an answer first and then reverse-engineer them? I know it doesn't make any sense but I know you get my point. Otherwise how do the score they contestants
3:20 LOOOOOL, Tibees made a Vines like monologue meme x-D Lovely girl 😀
Tibees: "Harvard Math tournament, I can't even!"
Me: "Waking up this morning, I can't even!"
Those are brain breaking questions. I just can't! LOL
My mind is now blown... My head a'splode....
Throwing √5 into a 'simple' parity problem gave me a a bit of a sardonic smile😼
For black squares: (32 choose 31) plus one way to occupy each white corner square = 32+2.
Repeat for white squares: total = 68
(10 seconds) ... next
They took Tough to another level.
Why not? you can do it!!!!!
At 3:05, u just need to “rationalise” the fraction using the conjugate of the denominator. As someone who “attempted” national olympiad before, this came rather quick but what to do after that, I also don’t know LOL. There are a lot of tricks which are glossed over by even the solution because it’s so obvious for those who are really familiar with math competition.
I never could understand complex mathematical equations , every-time i see it my brain shuts down
Nice earings!
everytime a see some maths problems like these I become happy and grateful my former self chose Physics over Mathematics in the college
3:20 I think it's not intended to the student to do all the questions. In the finals of a subject in my University they too do a test for you to choose three questions out of five, but it's way easier than that test. Therefore, there were people that could nail the five questions sometimes.
Your thumbnail and title absolutely crack me up! I am curious how Harvard and MIT prep their students for this tournament? Do you think there is some sort of prep meetings?
5 mins per question that s crazy