the fact that you begin from 1 + 1 = 2 and go all the way involving the Latin, the Greek letters and strange symbols, lines of math text, weird graphs, short sentences that require a lot of thinking and type stuff is amazing
@@rokoradic5153 this man trying to appear smart by essentially saying the OP has no idea what hes talking about when hes just talking about how advanced maths can get
@@off1cial_.19 bro he is talking about the weird letters, and he thinks the complexity lies in those... all im pointing out is that the letters themselves and strange words are actually easier to coprehend than you think, the difficulty of the problems lies elsewhere
Just do the first question. Its mostly critical thinking and not so math heavy. I can do it but probally cause I watched a ton of videos with similar questions
Dawg decimal digits refer to the digits in use for the base 10 system, ranging from 0 to 9.. it's there to prevent us from thinking about binary, octal, or hexadecimal number systems
I would give the length of my pillow but seriously who makes these absurd questions? No I wouldn't give the length of my pillow cause it is too personal
We know dio and jotaro hate each other so dio had to snatch them. He popped jotaros 3 baloons. 2+5 is 7 but pillows are for head so 7dm x 1dm is 7square decimeters
Even 2 weeks wouldnt be enough we had such ij my university back in the day when i studied complex math for aerospace and it killed me the exams were fair but the exercise troughout were just like those. U got a single exercise as big as 1/5 of a sheet for 2 fkn weeks and those 2 weeks still werent enough. Man im happy to be finished with that it was quite fun tho but desperate as well
Classwork:What is 2+2? Homework:what is 7x3? Test/Exam:If Bob has 12 apples,gives 2 to Jay,then what is the distance between the Sun and the Earth. SHOW METHOD.
@@elephorofonius the Astronomical Unit, or AU is unit of measurement. How do you define 1 meter? Well you probably don't know that either, it is defined as the distance light moves in 1/299 792 458 seconds. That is the scientific definition of the meter. Astronomical Unit, just like the meter, is a unit of measurement defined as the length between the Earth to the Sun. So my method is by definition, which is actually a valid proof in a lot of math problems some times.
Me during math questions: "Math question" *Me trying to solve it and concluded the answer is 24.* The answers: a) 500 b)450 c)350 d)300 Me: Obviously the answer is d.
IKR! ones I had a whole mental breakdown during naths and I asked my teacher here is how the convo went Me: mam...I have only 1 question. T: yes and that is..? Me: when do we actually use this? T: well buisness men- Me: no. They don't use "x" and "y" T: uhh T: honestly it's just for giving exercise for ur brains- Me: SO WE DONT USE THESE!? 😭😭
@@izukumidoriya4627 yo wait til you hear this- the only people doing this are math majors. additionally, everything in the world kinda runs on math, so instead of thinking about it as “i would never need to calculate the amount of watermelons jose has” think about it as understanding how the world works, from musical instruments to basketball to rocketships.
@@izukumidoriya4627 You will still need to know mathematics for doctor exam, also, instead of x and y what else are you going to use even the whole alphabets but you will still say its not necessary
I felt so smart knowwing integrals, derivates, square roots, cubic roots, big roots, trigonometry, areas of parabolas and senical, matrix and advanced statistics. Seeing those 5 exercises at the end made me feel dumb to what I have learnt of math, how can someone be such a genius?
The first one doesn't seem to hard honestly: To meet rule number (iii) N needs to be devisible by 2020*5=10100 and furthermore by 10100*11=111100. Now you can just add 0 at the end (= multiply by 10) creating legitimate numbers until you reach the limit of (ii). Or you can add blocks of 1111 in the front or a combination of both. Let's say the limit were 11 digits. Then there would be a total of 8 positive integers meeting all 3 conditions: 111100 1111000 11110000 111100000 1111000000 11110000000 1111111100 11111111000 Am I missing something? Obviously the notation must be mathematically correct in the test and you would need to calculate the amount of integers with a formula instead of simply writing all integers down like I did for this example.
me: happy about my 1/120 score on putnam that asian kid: crying about his 107/120 Edit: Holy cow this is getting insane. This is just a random comment I put on here. I did NOT expect this many likes and replies, let alone a literal war in the replies.
random thing from an asian: what you said about that asian kid cring about 107/120 is because for some reason asian parents always want the score to be high, only 5 or 6 questions wrong *for some reason*
Actually they are not that hard as a seventh grader I solved some an they are easy a bit I could say they average Asian can solve them they are easy I think 10 minutes will be enough
For those who haven't taken the Puntam, it's amazing how strict the grading is in terms of partial credit. You're expected to cover every single case, every possibility, all in great detail. It's easy to think "I think I got 1A" or "I think I understood 2B" only to get no points.
So basically you have to cover everything from the work, to the answer, to the possibilities, to why that certain possibility isn't the answer in like a proper English format making it extremely hard math + extremely hard english?
@@kit_ket1 Pretty much. I wouldn't say english is the hard part as much as covering your bases. You'll often have to prove statement X using technique A when variable z is even, technique B when z is odd, and technique C when z is exactly 0. Forget the 0 case or skip a step in its proof, and you can easily lose 9/10 points.
@@justkevinlol and express all the possibilities divided by your failure * the chance your dad is ever coming back with the milk all in enchanting table language
would you ever consider addressing MIT’s weird process of integrating freshman/finding roommates and things. I recently had a friend- who was a MIT freshman this year- who wasn’t able to find a roommate or a tribe. He ended up committing suicide just off campus last month. Of course it wasn’t the only factor involved, but what’s the process? is that sort of isolation and lack of support normal for MIT freshman ?
@@richie2033 probably some type of stereotype from the poc community that assumes mental health is not important and s*icide shows weakness Ik, I've experienced it
@@ArtwithariThechannelofart black people in IVY league colleges? What a joke. You could have a GPA much, much lower, and you’d be accepted into a IVY league instead of Asians. Forced diversity is the most American thing I’ve ever heard.
Lol same. I found the answer to the first one then realized the rest involved a version of calculus I didn’t know how to solve. Like some don’t even get an answer I just have no idea what they want it to be simplified to
Me: Ugh I hate math it's soo hard My parents: Math is like the EASIEST subject of all 💀 Edit: Okay, some people find math the easiest while some people say it's hard. It's easy if you're clear w/ the concept. It's hard when you tried a million times to solve a sum and it stills gives the wrong answer. End result? You get frustrated and hate it. So it really depends on your clarity of the concept.
Maths is fun, but exams make it seem hard and and irritating. I don't get High marks because of less time limit and tricky questions. But I can solve them when I'm not giving a paper because of zero nervousness and it's fun.
Depends on the difficulty. I scored 99.5 percentile in the JEE Main in maths, and I still probably would get a 0 in the Putnam. Edit: I'm now pursuing electronics and communication engineering at IIT Kharagpur :)
I majored in physics and took this test in undergrad with one day's preparation only because there weren't enough people to take it. It's so so fucking hard, because these are problems that require you to formulate your own proofs and really force you to think outside the box. It's pretty satisfying to get literally 1 single point, which is what I scored. Basically the exam is two parts with 6 questions each and iirc I sat for the exam from 8AM to 4PM on a Saturday. Each question is 10 points. Fun times:
You'll watch an entire Netflix show even when the first episodes are slow and boring just because someone told you "it gets better." *But what if you looked at your goals like that and watched your life get better instead??*
A5. Is too bad, we will do it together here we go. So the largest integer (n) such that ( an = 2020) happens when (n = boxed 14). This came from Zeckendorf's Theorem, which showed that every integer can be shown as a sum of non-consecutive Fibonacci numbers. (an) counts how many sets of Fibonacci sums equal (n), and the pattern shows (an = 2020) when (n = 14).
If anyone has seen the 3Blue1Brown video with the sphere and the random point and estimating how likely it is for the point to be in the pyramid that’s the final question on this test.
Or the underdogs could just cheat like MIT probably does it really helps when 3 of the people who come up with the problems for the test work at your school when harverd was dominating 2 of thoes people worked there. Cal tek is probably the most honist of the 3 highest scoreing schools
I remember watching a video that showed how to solve a question that appeared on that test. The question was something like : "4 random dots on the surface of a sphere form a pyramid (inside the sphere). What are the chances that the pyramid contain the center of the sphere?" It was very interesting to see how that person broke down that problem until it actually seemed possible, but on, there is no way I could get to the solution on my own in a middle of a test Edit: found that video if anyone interested - ua-cam.com/video/OkmNXy7er84/v-deo.html
Scientists have discovered that whoever looks at the Putnam Mathematical competition's questions , you'll receive headache, mild dizziness, stress and anxiety.
Class work - 2+2 Home work - 3 x 8 Exam - If the length of a pillow is 2 m and Tyler scores 4 marks in his exam. In how many years will your dad come back with the milk?
I once took an exam in 8th grade I don’t remember it’s name but it was incredibly difficult. There were about 50 questions for 100 marks for grade 8 to grade 12 and everyone had the same questions. I studied an entire year for that exam and didn’t know ANY answers. They had strict supervisors but I still managed to copy around 15 questions from a 12th grader and the answers were to be written on some sort of omr sheet and the answers were only supposed to be from 00 to 99. When I got my result I only got 1 question right for which I wrote a random number. So I wonder if it’s harder than this.
I love how in preschool there are barely any numbers in math and you are only getting introduced to it but when you progress to elementary it is mostly only numbers and then middle school is mostly numbers high school is less numbers and then college problems usually contain barely any numbers at all
We did this kind of thing in my high school. The concept was the same, but the questions were much easier than these. It was 6 questions, each harder than the last, and the questions were simple at their core but could seem complex from the outside. Also, the first question always did something with what year it was at the time. If you chose to participate in it, some teachers would give you extra credit for each point you got on it.
Its literally so easy A1. How many positive integers N satisfy all of the following three conditions? • (i) N is divisible by 2020. • (ii) N has at most 2020 decimal digits. • (iii) The decimal digits of N are a string of consecutive ones followed by a string of consecutive zeros. Solution: • Condition (i): N is divisible by 2020. This means N must be a multiple of 2020. • Condition (ii): N has at most 2020 decimal digits. This limits the size of N. • Condition (iii): The decimal digits of N are a string of consecutive ones followed by a string of consecutive zeros. This tells us the form of N. To satisfy all three conditions, N must be of the form: N = 111...11000...00 where there are 'k' consecutive ones followed by '2020-k' consecutive zeros. To make N divisible by 2020, we need to find the largest possible value of 'k' such that: 111...11 (k ones) is divisible by 2020. Since 2020 is divisible by 4, 5, and 101, we need to check if the number formed by 'k' ones is divisible by these factors. • Divisibility by 4: A number is divisible by 4 if the last two digits are divisible by 4. Since the last two digits of the number formed by 'k' ones will always be '11', it's not divisible by 4. • Divisibility by 5: A number is divisible by 5 if the last digit is 0 or 5. Since the last digit of the number formed by 'k' ones will always be '1', it's not divisible by 5. • Divisibility by 101: A number is divisible by 101 if the difference between the sum of the digits at odd places and the sum of the digits at even places is either 0 or divisible by 101. In the number formed by 'k' ones, the sum of digits at odd places is 'k' and the sum of digits at even places is '0'. Therefore, 'k' must be divisible by 101. The largest possible value of 'k' less than 2020 that is divisible by 101 is 101 * 19 = 1919. Therefore, there is only one positive integer N that satisfies all three conditions: N = 111...11000...00 (1919 ones followed by 101 zeros) A2. Let k be a nonnegative integer. Evaluate ∑ (2^k - j) * (k + j) / j! j=0 Solution: This problem involves a summation with a binomial coefficient-like term. We can use the following identity to simplify it: (k + j) / j! = (k + j) * (k + j - 1) * ... * (k + 1) / j! = (k + j)C(j) where (k + j)C(j) represents the binomial coefficient. Now, the summation becomes: ∑ (2^k - j) * (k + j)C(j) j=0 Let's expand the summation: (2^k - 0) * (k + 0)C(0) + (2^k - 1) * (k + 1)C(1) + (2^k - 2) * (k + 2)C(2) + ... + (2^k - k) * (k + k)C(k) Notice that each term can be written using the binomial theorem: (2^k - j) * (k + j)C(j) = 2^k * (k + j)C(j) - j * (k + j)C(j) The first part, 2^k * (k + j)C(j), corresponds to a term in the expansion of (2 + 1)^k. The second part, j * (k + j)C(j), corresponds to a term in the expansion of (1 + 1)^k. Therefore, the entire summation can be represented as: (2 + 1)^k - (1 + 1)^k = 3^k - 2^k Final answer: The value of the summation is 3^k - 2^k. A3. Let a0 = 7/2, and let an = sin(an-1) for n ≥ 1. Determine whether ∑ a^2n n=1 converges. Solution: This problem involves a sequence defined recursively and a series of its squares. To determine convergence, we can use the following steps: 1. Analyze the sequence: The sequence {an} is defined by an = sin(an-1). Since the sine function is bounded between -1 and 1, the sequence is also bounded. 2. Check for monotonicity: The sequence is not necessarily monotonic. It can oscillate within the interval [-1, 1]. 3. Apply convergence tests: Since the sequence is bounded, we can use the comparison test for convergence. We know that: 0 ≤ a^2n ≤ 1 Therefore, the series ∑ a^2n is bounded above by the series ∑ 1. The series ∑ 1 is a divergent series. Conclusion: Since the series ∑ a^2n is bounded above by a divergent series, it does not converge. A4. Consider a horizontal strip of N + 2 squares in which the first and the last square are black and the remaining N squares are all white. Choose a white square uniformly at random, choose one of its two neighbors with equal probability, and color this neighboring square black if it is not already black. Repeat this process until all the remaining white squares have only black neighbors. Let w(N) be the expected number of white squares remaining. Find lim w(N) N→∞ N Solution: This problem involves a stochastic process where we're repeatedly coloring white squares black. To find the expected number of white squares remaining, we can use a recursive approach: • Base case: When N = 0, there are no white squares, so w(0) = 0. • Recursive step: For N > 0, consider a white square. It has two neighbors. • With probability 1/2, the chosen neighbor is already black, and the number of white squares remains the same. • With probability 1/2, the chosen neighbor is white, and it gets colored black, reducing the number of white squares by 1. Therefore, we can write the recursive equation for w(N): w(N) = (1/2) * w(N) + (1/2) * (w(N-1) - 1) Simplifying this equation, we get: w(N) = w(N-1) - 1 This equation tells us that the expected number of white squares remaining decreases by 1 with each step. Therefore, w(N) = N - 1. Now, we can find the limit: lim w(N) / N = lim (N - 1) / N = 1 - 1/N = 1 N→∞ N→∞ Final answer: The limit is 1. A5. Let an be the number of sets S of positive integers for which ∑ Fk = n, k∈S where the Fibonacci sequence (Fk)k≥1 satisfies Fk+2 = Fk+1 + Fk and begins F1 = 1, F2 = 1, F3 = 3. Find the largest integer n such that an = 2020. Solution: This problem involves the Fibonacci sequence and counting sets of integers that sum to a given value. We can use the following approach: 1. Analyze the Fibonacci sequence: The Fibonacci sequence is defined by the recurrence relation Fk+2 = Fk+1 + Fk. This means each term is the sum of the previous two terms. 2. Explore the relationship between sets and sums: We need to find sets S of positive integers such that the sum of the corresponding Fibonacci numbers equals 'n'. Since the Fibonacci numbers grow rapidly, there will be a limited number of sets that satisfy this condition.
At first my English bad, so I can understand something wrong I not read all problems, but A.1 wrong. Answer is 508536. For example 111100 satisfies too and that the lowest suitable number. I not understand why we need 1919 ones in a row and I why look at divisiblility k ones in a row by 4 and 5 because if we add two zeros in, the end of our number it divisible by 20. Also I am not sure about your method of finding if number divisible by 101, you use method for 11
This isn’t taught or expected of in college. You don’t even have to take it. Every math problem in college or the useful real world is insightful and nice and “solvable”
"Dont worry guys, there are only 12 small questions for today's homework"
The 12 questions:
That's every assignment
@@footedsnow5682 if it’s every assignment eventually you’d learn
@@hanifziyadil8972 no like they don't teach what they had out
@@Socio_bros_garage yeah they don't do that here in usa, they just force us to memorize bullshit
@@vinson3725 I'm from the usa both of the schools I've gone to have done that
I'm more impressed by the people who made the questions for these tests
Coming up with questions to revise is hard man
that is exactly what i was thinking
it's most likely ai generated and then reviewed by real people.
@@crimsonszero oh interesting
@@crimsonszero nice thinking
If nobody is gonna get them they can just write a bunch of rubbish
If I had a cheat sheet for this, I’d need a cheat sheet for the cheat sheet💀
True😂
@@mohammedhussain4350 lol💀
Frr😭😭😭
and a cheat sheet for the cheat sheet for the cheat sheet
@@jpedrothejo And a cheat sheet for the cheat sheet for the cheat sheet for the cheat sheet
I got a 2 on it and won an award at my University haha. It was incredibly difficult.
You got an award for getting a 2? It really must be hard...
so many magicians are cubers 😂
Lol
Lol gg
shutup andrew
"What did y'all get on first question"
"69"
"96"
I somehow got French revolution as result.
I got radioisotope thermoelectric power generation, fucking help me out
I got Nuten's Law as the ans
@@SujitDas-hp3sj newton
@@sneed2600 he did it on purpose i guess
acually the answer is 4.7x^2
"This test is easy!"
The back side:
This test is the back side
💀
The lesson😀
The homework😬
The exam, 2 days after holiday:
Every Asian parents' dreams for their son: *YOOU HAVE TO GET 100% ON THIS!*
Didn’t laugh-
@AbES fr
You didn't have to laugh honestly :)
@@crazymonkee608 sounds a little racist ngl but you do you :)
But my parents are not like that man!
✨
the fact that you begin from 1 + 1 = 2 and go all the way involving the Latin, the Greek letters and strange symbols, lines of math text, weird graphs, short sentences that require a lot of thinking and type stuff is amazing
Nah you just dont know what half of those mean, if you did you'd realise why they're actually hard problems
@@rokoradic5153 this man trying to appear smart by essentially saying the OP has no idea what hes talking about when hes just talking about how advanced maths can get
@@off1cial_.19 bro he is talking about the weird letters, and he thinks the complexity lies in those... all im pointing out is that the letters themselves and strange words are actually easier to coprehend than you think, the difficulty of the problems lies elsewhere
@@rokoradic5153It’s the fact that they’re seemingly irrelevant but are involved that makes it weird. Stop being a prick
@@skibur848 how am I being a prick?
These the type of questions I'd fail to answer even with a cheat sheet
Me 2 😂
Bro forget the cheat ,if i had any maths book i want....
Still wont be able to do it
bro ur bringing a book, not just a cheat sheet 😂
Cheat with genius
Just do the first question. Its mostly critical thinking and not so math heavy. I can do it but probally cause I watched a ton of videos with similar questions
“Nice, I got a B+“
“What the fu-“
With grammar like “an B” it’s not a surprise you’re so in awe
I got a F- in gremar clas
@@theunknown4054 you should shut up I agree with you u.
@@Jakubboss99 an f
@@aqib8755 I meant to put that •_______•
the answer to the first question Is probably 0, because positive integers can't have decimal numbers
Dawg decimal digits refer to the digits in use for the base 10 system, ranging from 0 to 9.. it's there to prevent us from thinking about binary, octal, or hexadecimal number systems
By your logic it would be infinite solutions not 0
"This is the hardest question"
*shows us 2+2
Me: *hysterical laughter
Yeah i know right
it's obviously 6922420 lmao
@@mintyepicz noo, it’s obviously blue
If you're so smart then what's the answer?
@@mirrorhymn look at the replies
*That one question at the end wanting you to get only a 99% but not 100% during your final exam.*
I would tear up
Nah that question at the end worth 50% 😂
I was deadass one question away from a test and got 12/13 right
@@nooone1387 No, 99.999999999999999999%
Class : 3 + 5 =
Homework : 4 × 3
Exam : Jojo has 10 balloons, he gave 5 to dio. What is the length of the pillow?
Exactly 😂
My math class but divison on the exam and multiplication in class I don’t get homework for any of my classes
I would give the length of my pillow but seriously who makes these absurd questions? No I wouldn't give the length of my pillow cause it is too personal
We know dio and jotaro hate each other so dio had to snatch them. He popped jotaros 3 baloons. 2+5 is 7 but pillows are for head so 7dm x 1dm is 7square decimeters
Dio and jojo from the show that has the "your already dead" meme
You know you’re messed up when the smart keed starts crying and you ending getting a -10
Keed
--"So, why should we hire you?"
--"I scored a 2/120 in a Math test"
--"That's a shit sco-"
--"It was in PUTNAM"
--"Let's discuss salary, shall we?"
BAHAHAHAHAHAHAHA
lol
xD
Why does this remind me of that one scene from a movie?
That's the average score ,not fascinating
You know this is some serious shit when you get 6 hours for 12 questions
And with those questions it's extremely difficult to finish in that time
You would have to complete atleast 2 questions per hour to finish in time@Astromath
@@Faint236don't need to answer all of them to get 2 marks
Even 2 weeks wouldnt be enough we had such ij my university back in the day when i studied complex math for aerospace and it killed me the exams were fair but the exercise troughout were just like those. U got a single exercise as big as 1/5 of a sheet for 2 fkn weeks and those 2 weeks still werent enough. Man im happy to be finished with that it was quite fun tho but desperate as well
Classwork:What is 2+2?
Homework:what is 7x3?
Test/Exam:If Bob has 12 apples,gives 2 to Jay,then what is the distance between the Sun and the Earth.
SHOW METHOD.
1 astronomical unit. This is very general knowledge learned in like middle school, maybe earlier.
@@Cybrtronlazr wth, i’m in 8th grade and i have no clue what an astronomical unit is
@@Cybrtronlazr and what is your method?
@@elephorofonius the Astronomical Unit, or AU is unit of measurement. How do you define 1 meter? Well you probably don't know that either, it is defined as the distance light moves in 1/299 792 458 seconds. That is the scientific definition of the meter. Astronomical Unit, just like the meter, is a unit of measurement defined as the length between the Earth to the Sun. So my method is by definition, which is actually a valid proof in a lot of math problems some times.
@@Cybrtronlazr literally what language are you speaking
“Class Today we will be having a short 20 minute quiz”
The quiz 💀:
"The hardest math test"
The third question on Baldi's Basics : *Am I a joke to you??*
Yes you are right
Guys there is a game that is called Baldi's basics
Nope its 42 man its alien words aliens love the number 42.
The answer is 21
"add the recipe of cake with every element on the periodic table"
Hi
Hi!😊
most of the ingredients will have 0 grams lol
example: 0g flerovium
“Hey what did y'all get for Number 12?”
“I got 18”
“I got 9.5!?”
“I got Abraham Lincoln. For some reason”
Damn, I got a microwave
I got potato
I got a empty chip bag I’m now suing them bc I want chips now
That would be me 💅💀
I got house
My toxic trait is thinking i could probably do this
Me during math questions:
"Math question"
*Me trying to solve it and concluded the answer is 24.*
The answers:
a) 500
b)450
c)350
d)300
Me: Obviously the answer is d.
One of my people
My answer is 1
It happened in my computer exam my answer was 36 option was 70, 4, 45, 65 but dumb me did 65 when ACTUALL ANSWER WAS 45!!!!!!!!!!!!!!!
D
Same
"Professor when am I gonna use this in life?"
"Kid that's the point you dont"
IKR! ones I had a whole mental breakdown during naths and I asked my teacher here is how the convo went
Me: mam...I have only 1 question.
T: yes and that is..?
Me: when do we actually use this?
T: well buisness men-
Me: no. They don't use "x" and "y"
T: uhh
T: honestly it's just for giving exercise for ur brains-
Me: SO WE DONT USE THESE!? 😭😭
use it ur resume XD
@@izukumidoriya4627 yo wait til you hear this- the only people doing this are math majors.
additionally, everything in the world kinda runs on math, so instead of thinking about it as “i would never need to calculate the amount of watermelons jose has” think about it as understanding how the world works, from musical instruments to basketball to rocketships.
@@citratunealt1 *me who wants to be a doctor*
😅 yeah...let's think it that way~
@@izukumidoriya4627 You will still need to know mathematics for doctor exam, also, instead of x and y what else are you going to use even the whole alphabets but you will still say its not necessary
From what I've heard, only 5 people in the history of Putnam have gotten the perfect 120/120.
Should be easy if you study
@@joshy3671 yep i studied and got 120/120
@@joshy3671😂😂
@@tahaisboss1658 sat and act aren’t even remotely close…
@@tahaisboss1658
Like way beyond it.
I though you are serious when you show 2+2 💀
Like it's 22🤦🤦🤦
@@donniehill1383 uhm... No, it's 8
@@Cloudyyyyyy00 um, pretty sure it's 88...
you fools,the answer is 5
Guys, it’s 420. Get it right 😒
sheldon cooper: *Finally a worthy opponent, our battle shall be legendary.*
Omg.. so true ngl
OMG YES
Lol
Hello fellow children
I can't believe i found a Tbbt fan, 🥲 i'm glad i am not the only one who likes the show
Imagine being happy when u get a 1 or 2 on this that’s just crazy to think about
I felt so smart knowwing integrals, derivates, square roots, cubic roots, big roots, trigonometry, areas of parabolas and senical, matrix and advanced statistics. Seeing those 5 exercises at the end made me feel dumb to what I have learnt of math, how can someone be such a genius?
It's simple, they are not you, nor me
Bro I am 9th and wondering about your knowledge in maths that I should learn
@@flameofgamingvirtual3036 he really just listed stuff you learn in high school
@@mrocto329 Bros in year 10 prob
The first one doesn't seem to hard honestly:
To meet rule number (iii) N needs to be devisible by 2020*5=10100 and furthermore by 10100*11=111100.
Now you can just add 0 at the end (= multiply by 10) creating legitimate numbers until you reach the limit of (ii).
Or you can add blocks of 1111 in the front or a combination of both.
Let's say the limit were 11 digits. Then there would be a total of 8 positive integers meeting all 3 conditions:
111100
1111000
11110000
111100000
1111000000
11110000000
1111111100
11111111000
Am I missing something?
Obviously the notation must be mathematically correct in the test and you would need to calculate the amount of integers with a formula instead of simply writing all integers down like I did for this example.
me: happy about my 1/120 score on putnam
that asian kid: crying about his 107/120
Edit: Holy cow this is getting insane. This is just a random comment I put on here. I did NOT expect this many likes and replies, let alone a literal war in the replies.
Yeah if we don’t get above a 115 we literally get killed
Fr lmao
Lol, my friend did that test and scored 5/120
random thing from an asian: what you said about that asian kid cring about 107/120 is because for some reason asian parents always want the score to be high, only 5 or 6 questions wrong *for some reason*
Actually they are not that hard as a seventh grader I solved some an they are easy a bit I could say they average Asian can solve them they are easy I think 10 minutes will be enough
Schools " we don't put stress on our students!"
Also schools:
For those who haven't taken the Puntam, it's amazing how strict the grading is in terms of partial credit. You're expected to cover every single case, every possibility, all in great detail. It's easy to think "I think I got 1A" or "I think I understood 2B" only to get no points.
So basically you have to cover everything from the work, to the answer, to the possibilities, to why that certain possibility isn't the answer in like a proper English format making it extremely hard math + extremely hard english?
@@kit_ket1 Pretty much. I wouldn't say english is the hard part as much as covering your bases. You'll often have to prove statement X using technique A when variable z is even, technique B when z is odd, and technique C when z is exactly 0. Forget the 0 case or skip a step in its proof, and you can easily lose 9/10 points.
@@npharder Nah, it forces you to answer in fluent Latin
@@justkevinlol and express all the possibilities divided by your failure * the chance your dad is ever coming back with the milk all in enchanting table language
Bro gave us a math problem written in hieroglyphics
would you ever consider addressing MIT’s weird process of integrating freshman/finding roommates and things. I recently had a friend- who was a MIT freshman this year- who wasn’t able to find a roommate or a tribe. He ended up committing suicide just off campus last month. Of course it wasn’t the only factor involved, but what’s the process? is that sort of isolation and lack of support normal for MIT freshman ?
i’m really sorry about your friend. i hope you’re doing okay x
was he white?
@@swagmankayearIQ why would you even ask that
@@richie2033 probably some type of stereotype from the poc community that assumes mental health is not important and s*icide shows weakness
Ik, I've experienced it
@@ArtwithariThechannelofart black people in IVY league colleges? What a joke. You could have a GPA much, much lower, and you’d be accepted into a IVY league instead of Asians. Forced diversity is the most American thing I’ve ever heard.
Me watching 3 times to pause at the questions...
Lol same. I found the answer to the first one then realized the rest involved a version of calculus I didn’t know how to solve.
Like some don’t even get an answer I just have no idea what they want it to be simplified to
@@Name-ru1kt nice
Just pause the video and move the slider at the bottom to the end
@@ReflexRL It was before the feature was added, but ty for your help nonetheless
Me: Ugh I hate math it's soo hard
My parents: Math is like the EASIEST subject of all 💀
Edit: Okay, some people find math the easiest while some people say it's hard. It's easy if you're clear w/ the concept. It's hard when you tried a million times to solve a sum and it stills gives the wrong answer. End result? You get frustrated and hate it. So it really depends on your clarity of the concept.
Some are hard but some are easy
@@ikyz396 yup
Maths is fun, but exams make it seem hard and and irritating. I don't get High marks because of less time limit and tricky questions. But I can solve them when I'm not giving a paper because of zero nervousness and it's fun.
@@baldsoobinhair yeah..I find math fun because of the logics but these exams make me hate it
Depends on the difficulty. I scored 99.5 percentile in the JEE Main in maths, and I still probably would get a 0 in the Putnam.
Edit: I'm now pursuing electronics and communication engineering at IIT Kharagpur :)
My toxic trait is thinking I could do this
Im shaking by how difficult it is.
The intro made me throwup in my mouth and swallow it again.
😣🤮🤢😫
@@Gabo-tf2dx hell nah
🤢🤮🤑🤢
The money emoji is you swallowing it back like it’s cheese
@@PanlessXO lolll
Oh hell naw
*5 things to quit right now:*
*1. Overthinking*
*2. Trying to make everyone happy*
*3. Living in the past*
*4. Worrying*
*5. Doubting yourself*
Shut up spammer
@@omnipresentcatgod245 oh 😳
@@AhmetKaan dont listen to
omnipresent cat god You good
@@omnipresentcatgod245 NO, i need *YOU* to shut up
@@mm_ghost5489 why? Usefull tip are useless?
I majored in physics and took this test in undergrad with one day's preparation only because there weren't enough people to take it. It's so so fucking hard, because these are problems that require you to formulate your own proofs and really force you to think outside the box. It's pretty satisfying to get literally 1 single point, which is what I scored.
Basically the exam is two parts with 6 questions each and iirc I sat for the exam from 8AM to 4PM on a Saturday. Each question is 10 points. Fun times:
Sheldon will have fun answering this one 😂
This is like the written part of the chunin exams
from naruto its designed to trick you
Yes it was an activity in my high school Algebra 5 class and I have never died faster. Got a 2 in the calculus section!
You'll watch an entire Netflix show even when the first episodes are slow and boring just because someone told you "it gets better." *But what if you looked at your goals like that and watched your life get better instead??*
I will usually quit a netflix show on the first episode if I don't like it, guess I'm destined to fail.
TV shows usually get worse bro because they pull you a long and then have a crappy ending
Shut up
i don't even do the first one because i don't have the patience and just quit,
on second thought that's a good way to go about it
@@omnipresentcatgod245 that’s not really necessary
“The hardest question is 2 + 2= the colle-
Me: it’s 4
its 5
they were joking
Its 6 obviously 🙄
@@hello-Trick700 its 69420 duhhh
Actually it’s fish
A5. Is too bad, we will do it together here we go. So the largest integer (n) such that ( an = 2020) happens when (n = boxed 14).
This came from Zeckendorf's Theorem, which showed that every integer can be shown as a sum of non-consecutive Fibonacci numbers. (an) counts how many sets of Fibonacci sums equal (n), and the pattern shows (an = 2020) when (n = 14).
Me:76
A)22
B)27
C)25
D)29
Me: It’s 29 because that’s the closest to 76
If anyone has seen the 3Blue1Brown video with the sphere and the random point and estimating how likely it is for the point to be in the pyramid that’s the final question on this test.
I think that was for the imo which is for highschoolers
@@jasonwei9345 no it’s the Putnam which was made for undergraduates as a completition
@@kelpdock8913yeah there was a different video on an imo problem
There could be an anime bout this were the underdogs gotta eventually face MIT
Or the underdogs could just cheat like MIT probably does it really helps when 3 of the people who come up with the problems for the test work at your school when harverd was dominating 2 of thoes people worked there. Cal tek is probably the most honist of the 3 highest scoreing schools
That sounds like Assassination Classroom
I can hear my brain sizzling looking at these questions.
Q1: calculate the distance between the polar star angled at 90* to pluto.
Si
I remember watching a video that showed how to solve a question that appeared on that test. The question was something like : "4 random dots on the surface of a sphere form a pyramid (inside the sphere). What are the chances that the pyramid contain the center of the sphere?" It was very interesting to see how that person broke down that problem until it actually seemed possible, but on, there is no way I could get to the solution on my own in a middle of a test
Edit: found that video if anyone interested - ua-cam.com/video/OkmNXy7er84/v-deo.html
What the hell
So 4 dots, 1 pyramid, chance of containing the centre, sounds like the Putnam.
Takes one look
Me: gives up on life, I can barley do inequalities, bruh I’m in freaking 7th, like how?????????
Same oml 😭😭
I am in 10th and its the same situation rn -_-
haha don't worry, you'll get there eventually
When smart people thinks:0
When very smart people think:2
When someone guesses:
“here’s a few problems, good luck,”
*listen, i’m not lying when i turned off my laptop the second i saw all those numbers*
Bro the maths tests at my school are like "Sally has 204 apples, she ate 2.How many bananas does she have?"
Answer is 0 as Sally did not have any bananas as per the question prescribed above
@@sukii108 what if she already had two Bananas in her fridge? How do you know.
stop lying
the hardest math equation is
tuesday - 272 + wednesday x sky divide by how many leaves you can count during alien invasion
69
@@chiakinanami7573 😂😂😂😂👍👍👍
Imagien how smart those students are 😮. They are going to take the world one step ahead .
Scientists have discovered that whoever looks at the Putnam Mathematical competition's questions , you'll receive headache, mild dizziness, stress and anxiety.
Class work - 2+2
Home work - 3 x 8
Exam - If the length of a pillow is 2 m and Tyler scores 4 marks in his exam. In how many years will your dad come back with the milk?
underrated-
lmao
An Indian guy just walks in the class
Go away
The one kid that guessed all the answers, but somehow got A+:
Class: 6 + 1?
Homework: 12 × 11?
Exam: Alexander had 12 blackberries, and he gave 4 to his friend Lia. What is the shape of the box?
Box-shaped
@@asheep7797 that's some freaking weird + cringe answer dude 🤣
@@mk46gaming28 he isn't wrong
Math problems : Adam brought 69420 apples in an invitation. Tom played Minecraft for 69 hours. What is the diameter of the sun?
@@nairitsaren3781 answer: freaking huge compared to the earth
Whoever got that math test all correct, u are literally an Albert Einstein’s son
Ty
Do you mean AN Albert Einstein son?
u mean they got google
The teacher who made this test must be very intelligent
My ass is struggling to calculate normal algebra:
“It can’t be that har-“
Moments before regret
Bruv I like how it's all asians that dominate the exam 😂
Me when you said college students have 6 hours to complete 12 things me: that’s all my day in school!!!
It took me 1 sec to realize I ain’t doing that
Chat GPT: not all hero’s wear capes
I once took an exam in 8th grade I don’t remember it’s name but it was incredibly difficult. There were about 50 questions for 100 marks for grade 8 to grade 12 and everyone had the same questions. I studied an entire year for that exam and didn’t know ANY answers. They had strict supervisors but I still managed to copy around 15 questions from a 12th grader and the answers were to be written on some sort of omr sheet and the answers were only supposed to be from 00 to 99. When I got my result I only got 1 question right for which I wrote a random number. So I wonder if it’s harder than this.
Is it IOQM?
@@tomatoedits1138 no
Pre-Rmo is what you are talking about as for answers between 00 to 99
when that test is 100% of your grade
“Their favorite fifty cent song 12 questions”
This is the hardest math test: shows a image of two plus two.
Imagine some random Asian 5 year old just gets a 120/120
it is cringe when people think asians are like super computer
@@FA-ow4zs yeah 😂😂 thats not the case
@@FA-ow4zs they are because their parents are like hey if you don’t score a 100 on this test I’m getting the shovel
What I aim for
This is like a peace of cake of Asian college students 😂
Iam an Asian and not for me
Yes it was not toughest
the question creators are always smarter until you get all the way to the top and have to answer life itself
The questions be like: prove when the riemann zeta function equals 0
Gohar - This Exam is so difficult
*looks at bg video*
ME - YEAH IT'S REALLY SO DIFFICULT 😂
I love how in preschool there are barely any numbers in math and you are only getting introduced to it but when you progress to elementary it is mostly only numbers and then middle school is mostly numbers high school is less numbers and then college problems usually contain barely any numbers at all
the circle of me- i mean math
@@The_Blue_Ender aye im with u i get that
"this math exam is so difficult"
The exam :
This is exactly what I need to confuse my maths teacher
"heres some questions, good luck" man really thinks im gonna do this bullshit 💀
Holy fuck! Tbh this is really gonna take up more than 4hrs for me even as an engineering student
Is it really that hard?!?
These are math students, engineering students will have almost no chance if math students average a 2/120
I’m in 12th grade studying to apply to a good engineering college and this ain’t that hard
@@paarthjagga7287 If thats the case why do the most elite engineers struggle with this?
@@paarthjagga7287 LOL
if I even try one of those equations, I think my brains gonna fucking explode
My 8th grader ass is convinced i can do this easily
Sooo how did it go ☠☠
I am proud of myself for recognizing more than half of the math terms
You should be
We did this kind of thing in my high school. The concept was the same, but the questions were much easier than these. It was 6 questions, each harder than the last, and the questions were simple at their core but could seem complex from the outside. Also, the first question always did something with what year it was at the time. If you chose to participate in it, some teachers would give you extra credit for each point you got on it.
Great now my braincells vanished
You: 2+2 is the hardest question ever. Then me: it’s 4
Ok?
he was joking
@@calgames5557 he was joking too
Dont fall for someone trap
@@Youzw i know he was joking just that it wasn't funny at all, kinda cringe tbh
**pulls out picture math**
photo math*
“The Hardest Math Test Ever” I look at the thumbnail and be like-
The fact that people have gotten perfect scores on this is crazy
Its literally so easy
A1. How many positive integers N satisfy all of the following three conditions?
• (i) N is divisible by 2020.
• (ii) N has at most 2020 decimal digits.
• (iii) The decimal digits of N are a string of consecutive ones followed by a string of consecutive zeros.
Solution:
• Condition (i): N is divisible by 2020. This means N must be a multiple of 2020.
• Condition (ii): N has at most 2020 decimal digits. This limits the size of N.
• Condition (iii): The decimal digits of N are a string of consecutive ones followed by a string of consecutive zeros. This tells us the form of N.
To satisfy all three conditions, N must be of the form:
N = 111...11000...00
where there are 'k' consecutive ones followed by '2020-k' consecutive zeros.
To make N divisible by 2020, we need to find the largest possible value of 'k' such that:
111...11 (k ones) is divisible by 2020.
Since 2020 is divisible by 4, 5, and 101, we need to check if the number formed by 'k' ones is divisible by these factors.
• Divisibility by 4: A number is divisible by 4 if the last two digits are divisible by 4. Since the last two digits of the number formed by 'k' ones will always be '11', it's not divisible by 4.
• Divisibility by 5: A number is divisible by 5 if the last digit is 0 or 5. Since the last digit of the number formed by 'k' ones will always be '1', it's not divisible by 5.
• Divisibility by 101: A number is divisible by 101 if the difference between the sum of the digits at odd places and the sum of the digits at even places is either 0 or divisible by 101. In the number formed by 'k' ones, the sum of digits at odd places is 'k' and the sum of digits at even places is '0'. Therefore, 'k' must be divisible by 101.
The largest possible value of 'k' less than 2020 that is divisible by 101 is 101 * 19 = 1919.
Therefore, there is only one positive integer N that satisfies all three conditions:
N = 111...11000...00 (1919 ones followed by 101 zeros)
A2. Let k be a nonnegative integer. Evaluate
∑ (2^k - j) * (k + j) / j!
j=0
Solution:
This problem involves a summation with a binomial coefficient-like term. We can use the following identity to simplify it:
(k + j) / j! = (k + j) * (k + j - 1) * ... * (k + 1) / j! = (k + j)C(j)
where (k + j)C(j) represents the binomial coefficient.
Now, the summation becomes:
∑ (2^k - j) * (k + j)C(j)
j=0
Let's expand the summation:
(2^k - 0) * (k + 0)C(0) + (2^k - 1) * (k + 1)C(1) + (2^k - 2) * (k + 2)C(2) + ... + (2^k - k) * (k + k)C(k)
Notice that each term can be written using the binomial theorem:
(2^k - j) * (k + j)C(j) = 2^k * (k + j)C(j) - j * (k + j)C(j)
The first part, 2^k * (k + j)C(j), corresponds to a term in the expansion of (2 + 1)^k. The second part, j * (k + j)C(j), corresponds to a term in the expansion of (1 + 1)^k.
Therefore, the entire summation can be represented as:
(2 + 1)^k - (1 + 1)^k = 3^k - 2^k
Final answer: The value of the summation is 3^k - 2^k.
A3. Let a0 = 7/2, and let an = sin(an-1) for n ≥ 1. Determine whether
∑ a^2n
n=1
converges.
Solution:
This problem involves a sequence defined recursively and a series of its squares. To determine convergence, we can use the following steps:
1. Analyze the sequence: The sequence {an} is defined by an = sin(an-1). Since the sine function is bounded between -1 and 1, the sequence is also bounded.
2. Check for monotonicity: The sequence is not necessarily monotonic. It can oscillate within the interval [-1, 1].
3. Apply convergence tests: Since the sequence is bounded, we can use the comparison test for convergence. We know that:
0 ≤ a^2n ≤ 1
Therefore, the series ∑ a^2n is bounded above by the series ∑ 1. The series ∑ 1 is a divergent series.
Conclusion: Since the series ∑ a^2n is bounded above by a divergent series, it does not converge.
A4. Consider a horizontal strip of N + 2 squares in which the first and the last square are black and the remaining N squares are all white. Choose a white square uniformly at random, choose one of its two neighbors with equal probability, and color this neighboring square black if it is not already black. Repeat this process until all the remaining white squares have only black neighbors. Let w(N) be the expected number of white squares remaining. Find
lim w(N)
N→∞ N
Solution:
This problem involves a stochastic process where we're repeatedly coloring white squares black. To find the expected number of white squares remaining, we can use a recursive approach:
• Base case: When N = 0, there are no white squares, so w(0) = 0.
• Recursive step: For N > 0, consider a white square. It has two neighbors.
• With probability 1/2, the chosen neighbor is already black, and the number of white squares remains the same.
• With probability 1/2, the chosen neighbor is white, and it gets colored black, reducing the number of white squares by 1.
Therefore, we can write the recursive equation for w(N):
w(N) = (1/2) * w(N) + (1/2) * (w(N-1) - 1)
Simplifying this equation, we get:
w(N) = w(N-1) - 1
This equation tells us that the expected number of white squares remaining decreases by 1 with each step.
Therefore, w(N) = N - 1.
Now, we can find the limit:
lim w(N) / N = lim (N - 1) / N = 1 - 1/N = 1
N→∞ N→∞
Final answer: The limit is 1.
A5. Let an be the number of sets S of positive integers for which
∑ Fk = n,
k∈S
where the Fibonacci sequence (Fk)k≥1 satisfies Fk+2 = Fk+1 + Fk and begins F1 = 1, F2 = 1, F3 = 3. Find the largest integer n such that an = 2020.
Solution:
This problem involves the Fibonacci sequence and counting sets of integers that sum to a given value. We can use the following approach:
1. Analyze the Fibonacci sequence: The Fibonacci sequence is defined by the recurrence relation Fk+2 = Fk+1 + Fk. This means each term is the sum of the previous two terms.
2. Explore the relationship between sets and sums: We need to find sets S of positive integers such that the sum of the corresponding Fibonacci numbers equals 'n'. Since the Fibonacci numbers grow rapidly, there will be a limited number of sets that satisfy this condition.
At first my English bad, so I can understand something wrong
I not read all problems, but A.1 wrong. Answer is 508536. For example 111100 satisfies too and that the lowest suitable number. I not understand why we need 1919 ones in a row and I why look at divisiblility k ones in a row by 4 and 5 because if we add two zeros in, the end of our number it divisible by 20. Also I am not sure about your method of finding if number divisible by 101, you use method for 11
@@Davletov.ur right but im too lazy to change my comment
U are making me scared of going to college...
Lmao you don't have to take it.
This isn’t taught or expected of in college. You don’t even have to take it.
Every math problem in college or the useful real world is insightful and nice and “solvable”
Just take business like me . Free and easy . Don’t need to always do calculation but u have tons of assignments haha 😂
Same, college seem brutal, the subject, the math, the fee,
I dont even remember writing this comment lol
Im in college now
You have a better chance of guessing the answers than doing the math
Yeah 2+2 is very hard indeed
This is the average asian student's homework