Unlocking Your Intuition: How to Solve Hard Problems Easily

hi you may have seen videos like this or this or even some of my own stuff and you probably wondered how how is a human like you or me capable of being so fast at something and how can you get to this point too and as it turns out nothing special is really happening just as you can instantly recognize the smell of your favorite food people who are really good at things can instantly recognize the solution to a familiar problem it's like second nature So today we're going to cover how this happens and talk all about intuition a lightning fast super powerful intellectual part of your brain that works unconsciously almost like magic to brew up solutions to any sort of problem you're trying to solve and if you practice and use it properly which I'll show you how to do you can train yourself to find solutions to very challenging problems and mere seconds and yes this is intuition for problem solving any kind of problem solving and while I'll be talking mainly in the context of programming as applies to basically anything competitive programming coding interviews math chess even I don't know anything even real life problems and this video you you're going to learn how you can use it to its full potential now obligatory saying that's not the flex but just to prove my credibility there's a reason I'm qualified to talk about this for one I'm one of the world's best competitive programmers so I know what it takes to get good at problem solving and I'm very very good at speed contests and the reason why is that my intuition is extremely strong and I can come up with a solution to most problems basically instantly so you can trust me to talk about intuition too but we'll focus on one particular achievement here so yusico is this national USA competitive programming competition with a lot of people it's like the math Olympiad for programming and in just three months I got to the top 10 percent or the highest division how I use two strategies the first was raw practice and I've talked a lot about that in other videos but the second was something I've actually never spoken about before it was a purely intuition-based strategy and it worked way better than I expected it to I think it really did unlock my intuition and it'll certainly work on yours too so I'll deep dive into that strategy later in this video now let me just describe what I mean by intuition since people tend to group terms together and have different definitions there's a little bit of science I'll have to involve here but it'll be quick I promise it's probably also an oversimplification but it'll work here it's fine so imagine your brain has two sides to it a fast side and a slow side your slow side is the thinking that you put effort into it's your processing and your reasoning and hopefully decide you're watching this video with and your fast side is what's relevant for intuition it's your fuel based thinking it's the patterns you learn and it's completely unconscious you don't have to mentally activate it it doesn't take any work and a consequence of it being so fast is that it has to be based entirely on just your past knowledge and your knowledge of the situation in front of you there's no other information you can use because you don't have time to think so the more knowledge you absorb the more accurate your fast brain would be and intuition isn't the entirety of your fast brain it's only a part of it but everything about the fast brain applies to intuition more knowledge more effective so to summarize intuition basically asks given a problem what has worked before will it also work here that's all it's doing it comes as a gut feeling as you probably experienced and I can explain in an intuitive way too by the way the word intuitive it means that it makes sense to your intuition and the easiest way to think about intuition is like a sixth sense look at this image a lot of things just happened in that Split Second your brain went through an incredibly complex series of calculations and all of that came together for you to recognize that I just showed you a chair and that's stupid and pointless but the idea is your sense of sight lets you easily recognize objects without even thinking about it intuition works the same way you encounter some problem without even trying your brain tries to categorize it based on other problems that it's seen before if I give you a different type of chair even though it's not the same your brain still does a pretty good job of categorizing and similarly if a problem has any similar elements to other problems you've seen before you can recognize those elements and put them together to work on a solution I've caught myself countless times saying something like smells like greedy or feels like binary search or something of that nature and it really does just smell think of intuition like a sense and it'll make sense I'm sorry now there's one distinction I have to make there's intuition and insight different terms that kind of mean similar things so I should clarify what I'm talking about but intuition is part of your slow brain it's hard to tell whether it's unconscious or not but it's more towards the side of deep reflective thought rather than the instant intuition and it generates new solutions to problems rather than offering old ones to imagine this better imagine a completely random sequence of characters there's a decent chance that you'll find a few actual words in there and that's a massive oversimplification of how Insight works but given the random noise of your thoughts some of it will be incredibly useful and new to you and I won't go any deeper let's just get back to intuition and hopefully I've done a decent job at selling intuition to you but there are a few explicit reasons for why it's a good thing to develop your intuition first there are obvious benefits to being able to solve problems quickly especially for time-based problems where it's really helpful to get quick Solutions intuition is your wingman into the world of success it's pretty much the fastest brain process that'll be useful to you so it's good for you until tuition to be strong and your intuition is generally going to be the first thoughts that you think of these thoughts will likely take up a lot of your time so it'd be a good thing if your intuition was strong and those thoughts were correct and even Beyond just the first step your intuition can guide you through the next steps and the next steps after those and for all of that you want your thoughts to not be wrong so having a strong intuition is always good if you don't have the right intuition even if your slow brain is really strong you'll be fighting yourself the whole time because you're fast brain and your intuition will be screaming wrong ideas at you and there are of course more reasons for wanting a good intuition but you get the point now there are some important things to mention about actually using intuition first you have to work with it not rely on it intuition only generates shallow ideas it gives you a step in the right direction but it doesn't give you the full directions unless the problem is simple enough that each idea can be figured out by intuition you can take the ideas that intuition gives you and expand them into a full solution but you likely have to do that with your slow brain and your reasoning so make your fast burning slow brain work together get ideas from intuition and details from reasoning and also you should be wary of the fact that your intuition could be wrong you should try to back up your intuition with either actual justification or proof even or at the very least some small example cases for this it does help to be good at proving things you obviously don't have to be formal there exists things called intuitive proofs that are based on intuitive facts that make sense to you and you can just take the big ideas and leave out the small details but it's a good idea to practice justifying things otherwise you'll likely just be making semi-blind guesses from intuition which won't always work out for you and while intuition is great for pointing you in the right direction sometimes it points you in the wrong direction too and the issue with intuition being wrong is that it's quite hard to tune it out if your intuition is wrong and you have to work with some unintuitive idea your intuition will be screaming at you to go some other way and it won't be good it's easy to get trapped in a wrong idea for your intuition and struggle to get out of it so be careful with it again that's why it's a good idea to get good at proving stuff because logic is a separate way to check if your intuition is misleading you or not and the better you are a logical thing thinking and reasoning the better you'll be at ignoring wrong intuitions because you have practice with working independently of intuition so intuition is usually good but not always sometimes it's better to stick to Pure logic and that's why it's important to improve both and not rely on one too much intuition is also unconscious you can get an idea but have no idea where I came from sometimes it's even harder to understand how you got the idea than to come up with the idea itself and that sounds pretty annoying but you can still work with it because eventually The Logical side of your brain will come to the same conclusion and that's a conclusion that you'll understand a lot better so it's not such a big deal and finally intuition is not so useful for entirely new stuff as again it's based mostly on past information other things can help you with that like logic or Insight but intuition won't do much for you but it's damn good at recognizing stuff you've seen elements at before now as I mentioned in the beginning there's an intuition-based strategy I use to achieve super rapid Improvement in yusica and the main reason I didn't share it before is because I thought it didn't help me but after thinking about intuition a lot for this video I realized that it did a lot more for me than I initially thought and what I did is really simple I picked a bunch of problems from the hardest Division and second hardest problems that were admittedly way too hard for me and I didn't even attempt to solve them all I did was read the problem and then almost immediately have to read the solution and my thought process when doing this was I have a contest soon and I need to learn as much as possible so let's become familiar with a bunch of different problems and different solution ideas and if I see anything similar in the contest I can look at this problem and its solution again and figure out how it can help me and admittedly this won't work for youseco anymore because you can't use the internet and problems are less topic oriented now you can take the basic idea of what I did and turn it into a general strategy basically what happened was that I created a mental mapping between problems and solutions but not really problems and solutions more like problem components and solution components like General problem components to General solution ideas and that's exactly what intuition gives you General ideas the strategy breaks down information the exact way that your intuition will process it and you should include everything about the solution not just the solution itself but also elements of how to come up with it thought-provoking questions to ask yourself simplifications you can try common thought processes Etc anything that could possibly apply to Future similar problems it also helps to understand why the associations actually work this will make your intuition more accurate since it lets your intuition understand what it's doing and also tells it what information is more relevant and what information isn't and if you end up finding that none of your associations can justify the solution it tells you need to look for new associations in the problem it's not strictly necessary to understand the whys and ultimately you're just learning patterns but it helps so to generalize the strategy to this video you want to break down the problem and solution to pieces that are easy to remember ideally plain English or whatever language you prefer and then learn or memorize but ideally learn these pieces and create the mental Association so when you encounter similar problem pieces your intuition can easily match them to the appropriate solution pieces now it's significantly easier to remember stuff if you come up with a solution yourself since your brain will already understand it and you remember it better still if you spend time on the problem because the more time you spend thinking about it the more it'll be burned into your brain and further still solving the problem helps you to understand the why between the behind the associations and that helps your intuition be more accurate which can help a lot so it's up to you you can either solve problems normally and also create the mental mapping to help your Intuition or you can use the strategy I use myself and not even bother solving just create the mental mapping the slow strategy of actually solving problems will give you deeper understanding of solutions and improve your logic too while the fast strategy of jumping to Solutions will help your intuition more but nothing else so there are trade-offs and you can try both and see what sticks with you more but no matter what you do you want to create that mental mapping for every problem you do that's what's going to help your intuition and you may also want to do some explicit testing of your intuition too I have a video on this for the programming world but the gist is give yourself a problem and try to guess only the high level General ideas see if your intuition is right about them and do that for a lot of problems and if you don't understand something or get something wrong try to use a proof for justification or solve it fully so you can see why that's the answer and why you got it wrong but ultimately just give your intuition that exercise and separately you also want to challenge yourself because you won't learn much from stuff that's already easy for you I did my process and problems that were extremely hard for me there's some Merit to practicing easier problems for the purpose of getting faster and you may want to do some of that too but speed will come naturally anyway so don't worry too much about that and also note that there are a lot of parallels of pattern recognition you're creating mental patterns for yourself so your intuition can pick up on them and recognize them in similar problems so being good at that will help too and there's roughly three more things to mention in this section first I want to make it clear that you can't do only the mental mapping strategy if you your intuition is extremely far ahead of your reasoning skills you will be lost all the time you have to do normal practice too because for the hardest of problems your slow brain is going to do most of the work I also said before to properly use intuition you also have to be decent at proving or justifying your intuition to make sure you aren't being led down a wrong path so while training your intuition when you're solving problems make the effort to justify them too learn proof techniques and get some proof practice too so you can tell the difference between wrong and right intuitions and one final thing there may exist some research to stuff like meditation or mindfulness training helps I can't really comment on it but I felt like I bring it up so feel free to try it or research it more for yourself if you want now one more thing let's address the common concern about intelligence will smarter people have a natural Advantage with intuition obviously there will exist people that have better intuition than others and can improve it faster but the more interesting question is why that's the case one answer is that some people have a natural advantage over others but is it really natural in the common nature versus nurture debate in science I like to believe in nurture and the reason that nurture is nice is because you can change it it's optimistic suppose hypothetically that nurture completely wins and your ability to reason into it is based entirely on your past experience stuff like your education how much you've been exposed to challenging problems then some people who have had better and more intellectually stimulating educations will be better problem solvers and have better intuition and that's cool and expect it but no no matter what's happened in your past you have control over your future if you expose yourself to challenging problems now and properly train your intuition now the future you can have powerful intuition too so in a hypothetical world where genetics mean nothing and everything depends on past experience you can shape your Futures Past by shaping your future and therefore shape how strong your intuition and intellect even will be in the future and that means you have full control of your life which is a great thing to believe and you should try to convince yourself that even if you don't already believe it because it's just a good way to think but obviously it's not a hypothetical world and genetics probably do matter some but there's also no way that's 100 genetics and I tend to believe that nurture plays a much bigger part and let's delve deeper into this because why not this can be motivational in the world of competitive programming and almost certainly in different problem-solving oriented communities too A lot of people like to blame stuff like IQ for the reason they aren't improving and sure IQ research correlations blah blah whatever but what is IQ really it measures your ability to reason and how do you learn to reason nurture practice experience and ultimately the majority of your past experience boils down to roughly two two main things your parents and your education if you're later on in life replace that with work or life experience and if you've been problem solving for a while you can consider that problem solving to be your experience you can use my success story as an example I got lucky and got the good side of everything I was fairly challenged when I was young and in that sense I also had a really good education and was constantly in classes that were actually interesting and hard at least for Math and the most important thing I had the passion I care deeply about competitive programming that's how I got so good at it because passion is super duper important if you don't have it you have to hold on to whatever reason you have for doing this kind of stuff this problem solving because a motivated brain is so much more effective I think a lot of lack of improvement in the world comes from people trying to force themselves to do things they don't care about because if you don't care your brain won't care about improving so you can either switch to something you do care about or convince yourself to Care by focusing on the end result but getting that mental interest is huge you don't have control of your nurture in the past but after watching this video consider yourself enlightened you now have the ability to control your future your ability to reason and Intuit is now in your hands because you can choose how you use your time to improve and now after all that hopefully you have a maybe Newfound belief that practice will pay off since you're really just controlling your own nurture for the future and playing into the science and now that I've also gone over how you can improve your intuition you're all set to to get started now one thing I will admit is that my brain is pretty good so my technique of memorizing solution ideas and problems I had barely read will likely not work for everyone and that's fine and that's expected as I said you will do fine with solving problems normally but doing a bit of extra work to train your intuition too the main takeaway from this video is that extra step making sure you're creating that mental mapping between problem components and solution ideas another takeaway there's an idea I like that your intelligence is only in your hands once you believe it is otherwise if you don't believe you won't do anything about it well now's your time to believe take control of your fate if you blame your skills or lack thereof on some external Factor even if it's true it's not helpful do what you can for yourself and you'll be the best you possible that's generic but it's it's true I mean it's true and one more thing if you've watched some of my past videos I strongly advised against a strategy like this am I contradicting myself and the answer is yes and no because the point of my advice in the previous videos was to emphasize that good practice is what matters if you get good practice you will improve if you do other things along with good practice like the mental mapping strategy you will still improve and maybe you'll even be specialized in intuition so overall I think my old advice still a prize applies you should get good practice and this strategy should absolutely not be the only thing you do but I think the strategy can help and combined with good practice it can work for you and there's also the obligatory this is just an opinion thing but this is at least backed by both research and experience I I think it's fine and that's all goodbye

Channel: Colin Galen

Views: 1,198,032

Keywords: how to use your intuition, what is intuition, power of intuition, intuition, unlocking intuition, problem, solving, problem solving, math, chess, programming, competitive programming, codeforces, speed, speedforces, speed contest, how i solve hard problems quickly, intuition problem solving, problem solving intuition, how do people solve problems quickly, solving quickly, seconds, minutes, solve hard problems in seconds

Id: 1f6N2UrCK6o

Length: 17min 33sec (1053 seconds)

Published: Wed Nov 09 2022