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/sci/ - Science & Math


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15755791 No.15755791 [Reply] [Original]

Whatever school math has taught has clearly not been enough to solve those nutty critical problems that don't require you to differentiate or integrate a function.

I've recently been going through Paul Zeitz's The Art and Craft of Problem Solving, and I realized that I withered away my time for nothing. That book is what I NEEDED all this time. It however is unfortunate that I'm a complete retard who's struggling to even solve the first few questions of the book.

For example, this question" Find the next member in this sequence 1, 11, 21, 1211, 111221,…" yeah I can't solve this, and the solution is pretty difficult to understand. With that said, some of the previous questions have made me go "OH SHIT WHY DID I NOT THINK LIKE THAT"

Now please tell me how I can train myself to get better at these kinds of problems, which is what mathematical olympiads all seem to be about. Also suggest some books that are in a similar vein to this as I couldn't find a single resource that aims at the target this book aims for.

>> No.15756271
File: 104 KB, 458x350, chrome_2023-09-19_14-06-27.png [View same] [iqdb] [saucenao] [google]
15756271

>>15755791
just learn to solve problems bro.

>> No.15756289

>>15755791
you sure do seem to like talking about yourself on social media

>> No.15756534

First thing first, you should learn that "problem solving" is a meme word. Do you know why?
>For example, this question" Find the next member in this sequence
This is not a real problem, this is merely a quiz. You wanna know real problems? World hunger, poverty, diseases, human rights violations, pollution, criminality.
I'm sure as hell mr Zeitz have no solution for any of this. So, fuck off.

>> No.15756905

>>15755791
You shouldn't be able to solve that sequence from the get go
Zeitz said in one of his videos that the question was brought up by two IT guys who were working in the same university as he does, they told him they couldn't find the next number in that sequence even after days of thinking, when Zeitz looked at the sequence, it took him only minutes to figure it out
He said that

>> No.15757042

>>15756905
well so how do I train myself to become like zeitz?

>> No.15757046

>>15755791
>How the fuck do I train myself to get better at "problem" solving?
Make ot life or death. Actual life or death.

All your delusions and ego disappear when you realize youre about to die...that is where your Truth will be found.

>> No.15758990

>>15755791
>some of the previous questions have made me go "OH SHIT WHY DID I NOT THINK LIKE THAT"
It's because there is a framework to solve problems like these that you haven't learned yet. Just find it out, then most of the problems will reduce to maybe a couple different ones.

>> No.15759003

>>15755791
LMAO, problem solving is so easy. If you actually got a real job for once you'd realize the actual hard problem (kek) is problem DEFINITION.

Many people are absolutely hot wet garbage at describing their problems effectively and providing the information they have in order for someone to solve it. This is why medicine has so many complications. Problem solving is straight forward, but try solving an undefined or poorly defined or incorrectly defined problem and you'll see how valueless it is.

>> No.15759021

>>15755791
Can you upload it here or post the link?

>> No.15760277

>>15755791
You git gud by solving problems. Over time you build a stock of thinking strategies and notions and tricks that recur again and again, and generalize whole classes of problems. There's no shortcut to develop that but it's worth it, it's one of the few skills that transfers to other fields. You learn to simplify things and spot patterns.
At first you'll probably look up the solutions often, don't worry about it and don't become frustrated by your own brainletism, not everyone's a von Neumann. Just make sure to understand the solutions thoroughly and extract the main insights from them.
There are many good collections to train, eg Smullyans or Gardners books, Dover has some good ones, there are collections of olympiad problems online...

>> No.15762302

ok, so i solved in my rest time between sets at gym. here how it goes: you ad every next number to the previous one and the previous one is going to the right side and you move 1 from the next number on the front. 11+21=1211 because u add 11 on the back of the whole number and u move 1 from 21 on the front. 1211+21=111221 because you move 11 on the front of 1211 and you add 21 to the back of the number so its 111221. 111221+1211=11112211211 (I might be wrong but it makes sense to me)

>> No.15762305
File: 77 KB, 828x821, 1691061693857615.jpg [View same] [iqdb] [saucenao] [google]
15762305

>>15762302
>(I might be wrong but it makes sense to me)
Ride on, space cowboy. Youre gunna carry that integer...

>> No.15762320

11112211211

>> No.15762537

>>15755791
Just ignore the problems, bro. Not having a problem is a solution, too.

>> No.15762586

>>15762302
I developed a logical continuation of 1s and 2s as well, and you're also right to do so, since problems like the one OP mentioned have multiple solutions without any further clarification.
But if you google this exact sequence, you'll see the solution is a lot smoother.

>> No.15762633

>>15755791
Post excerpts

>> No.15762820

>>15756534
who hurt you?

>> No.15762872

>>15755791
Pretty fucking easy
>1,
There's one 1
>11,
There are two 1s
21,
There is one 2 and one 1
>1211,
There is one 1, one 2, and two 1s
>111221
There are three 1s, two 2s, and one 1
312211

As a reward, explain what the book teaches. Is it really good?

>> No.15762879

>>15758990
>framework to solve problems
This is the exact opposite of problem solving. Go read up on how Kepler found his laws. I promise it's interesting.

>> No.15762930

>>15756534
LMAO, those are not problems, those are solutions to cull down overpopulation.

>> No.15762933

>>15762879
Sometimes you gotta create the framework yourself but alright, I'll trust you.

>> No.15763783

>>15762933
In that case the framework is the solution.

>> No.15763830

>>15755791
Reincarnate and spec into high IQ class next time.

Alternatively wait for a mid-game respec option to be added to this game, might take a while given current genetic therapies though.

>> No.15764088

>>15755791
Where epub?

>> No.15764127

>>15762872
This is the low iq solution. The high Iq solution is to fit a polynomial to the sequence, obviously.

>> No.15764261

>>15764127
Zeitz said John Conway could come up with a theorem for that sequence, which involved a 73 degree polynomial equation

>> No.15764630

>>15764127
Fuck you, meanie.

>> No.15764845
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15764845

just solve lots of different problems and learn different ways to approach them. You need experience
also, 312211

>> No.15764868

>>15764845
How tall are you?

>> No.15764881

>>15764868
whats that have to do with anything?

>> No.15764902

>>15756289
Shut up nigga. I left and came back and your incel ass is still here

>> No.15765089

first entry is 1. First entry, counting from the left, has a consecutive block of length one of 1's, so the second entry is 11 (one 1). Second entry has a consecutive block of length two of 1's, so the third entry is 21 (two 1's). Forth entry will be 1211 (one 2, one 1)fifth will be 111221( one 1,one 2, two 2's). six entry will be 312211 (three 1's, two 2's, one 1)

>> No.15766440

You are all a bunch of negros

>> No.15766447

>>15755791
Good problem solving skills require good intuition. Unfortunately, even if intuition can be imrpvoed, nobody really knows how. And if anyone claims they know, they're probably lying.
The best you can do is go and try to solve multiple similar problems to get the gist of it. Also accept that some people are just naturally good at problem solving.

>> No.15766449

>>15755791
Break the problem down. Look at the core components, potential causes, and then work up from the most basic to most complex. Where people go wrong often is starting at too complex of a solution by making assumptions and they get lost in details. Most of the time, the cause is much more basic than assumed.

>> No.15766818

>>15755791
the next number is 312211

>> No.15766833

>>15755791
I just solved heaps and heaps of problems as a kid, I had friends who were also good at mathematics and we made problems and gave them to each other to solve, sometimes it would take days of just thinking about the problem and eventually you just "get" it, kind of like a eureka moment (better feeling than orgasm btw). There's a lot of general advice about problem solving but I don't know anyone who actually uses it consciously. For example, you may find a problem in 3D easier to solve if you first think in 2D, or a problem sometimes is easy when you provide an algebraic model, or you may think of specific subcases of a more general principles and use that to find a pattern and so on, you kind of just pick this stuff up automatically and do it "subconsciously" in real life.

The problem with some of the olympiad problems in particular is that they also assume a certain curriculum, for example, you're supposed to know a whole truckload of inequality identities (and subsequently practiced using them hundreds of times) whereas if you're coming from a normal advanced high school mathematics background, then Putnam is probably easier to get into. Go here: https://prase.cz/kalva/putnam.html and start at 1938, enjoy.

>> No.15767039
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15767039

>>15755791

>> No.15767043

solve problems to get better at "problem solving" (whatever you want that to mean)
Btw that book is a meme, I used it and it was not only boring but it didn't help that much, it helped much more to solve problems without the intent of learning to solve problems

>> No.15767344

>>15766833
>better feeling than orgasm btw
How would you know that? Anecdotes from friends don't count.

>> No.15767876

>>15766833
>better feeling than orgasm btw
this is the most childish and stupid thing I've heard in long awhile. how can you think of such a comparison?
even tho I'm virgin I'd never say doing math is better than an orgasm

>> No.15768348

>>15755791
>I couldn't find a single resource that aims at the target this book aims for.
I think there's that Presh Talwalkar guy who specializes in math problem solving. He has a YT channel and some books. Not sure how helpful he is, though.

>> No.15768397

My answer is 11112211

>> No.15768531

>>15767039
this chart is so fucking gay
>a start
>a taste
>a prime
>a beginning
what's next?
>a nibble
>a warmup
>a foreplay
>a tryout

>> No.15768735

>>15755791
>add 1
>add 2
>add 1 and 1
> add 2 and 1
>add 2 and 1+1
111122211

Sequences like these are pretty stupid. The solution is not guaranteed cause the logic only implies a general pattern continuation which has indefinite different fits

>> No.15769002

>>15767344 haha funny
>>15767876
>t. never solved a hard problem

>> No.15769596

>You wanna know real problems? World hunger, poverty, diseases, human rights violations, pollution, criminality.
We both know the solution to these issues, let's be real. But good luck finding someone who has the balls to make it a reality.

>> No.15769617

>>15769596
Where's Thanos when you need him?

>> No.15769775
File: 347 KB, 699x602, 1693483985382430.png [View same] [iqdb] [saucenao] [google]
15769775

brainlet bros... why do we keep on getting dumber with every passing year...

>> No.15769776

>>15769596
Curb that antisemitism.

>> No.15769914

>>15769775
That's just the thin veil of naïvety lifting and you observing the stupidity of reality. I'm sorry, the utmost majority of people put there are borderline retarded. Now you know why elites exist and why they are important.
Brave New World is not a dystopia if you actually read it to the end.

>> No.15769924

>>15767876
not him, but the moment of understanding something that eluded you for quite a while can throw you into such an euphoric state that certainly no orgasm compares to, maybe only an intense feeling of love does.

>> No.15769938

>>15769596
>'we' know it
>doesn't say what it is
every time

>> No.15769980

>>15764088
pdfs there on libgen

>> No.15770016

>>15755791

312211

Honestly took me 30 seconds

Where is my medal?

>> No.15770062

>>15769980
Yeah, but they suck on e-readers.

>> No.15770071

>>15755791
The whole point of the look and say sequence is that it's very hard to see until somebody explains it to you, because it's such an off-the-wall way of producing a sequence of numbers that you probably have no prior experience with anything like it. You get the same experience tons of times practicing for olympiads.
Mathematical "problem solving" in the sense of olympiad stuff is a sport. You train for it by practicing problems until you can recognize similarities in them.
The goal way to win an olympiad is to come up with exactly nothing on the fly. If you're relying on ingenuity to save you, it's because you haven't done enough similar problems to have good ideas about what sort of things might work.

If you want something like a slightly easier version of Zeitz the Art of Problem Solving books are excellent and essentially start from zero prior contest experience.