The Ultimate Problem–Solving Strategy | My Secret to Winning Physics, Math, and Coding Competitions
The Ultimate Problem–Solving Strategy | My Secret to Winning Physics, Math, and Coding Competitions
The Feynman technique for solving complex problems. Problem-solving strategies which I used at the International Physics Olympiad, as well as many math and coding competitions. This is a general strategy, which you can apply almost anywhere. Including business problems, exams, competitions, …
▬ In this video ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
I talk about why becoming a great problem solver is probably THE most useful skill you can acquire in your professional life. I talk about the Feynman strategy (or technique) for solving complex problems.
The Feynman strategy goes as follows:
1. Make sure to fully understand the problem formulation and what kind of solution you need to find
2. Explain what you know and break it down into smaller problems. Talk to other people, and try to close your knowledge gaps, until you eventually solve the problem.
3. Write it down and memorize it (check out my video about this: • Best Study Method if You Struggle to … )
▬ Watch this next ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
Video about understanding math intuitively: • How to Understand Math Intuitively?
Video about memorization techniques: • Best Study Method if You Struggle to …
Video about my Ph.D. research (Quantum AI): • Quantum Artificial Intelligence | My …
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▬ Wanna know more about Richard Feynman? ▬
Check out Feynman’s fascinating biography: https://en.wikipedia.org/wiki/Surely_…!
Or Feynman’s famous lectures on Physics (this is advanced college level): https://www.feynmanlectures.caltech.edu/
▬ Timestamps ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
0:00 - Intro
1:45 - Become a great problem solver!
2:40 - Practice problem
3:03 - Step 1 of Feynman’s strategy
3:41 - Step 1: example
5:01 - Step 2 of Feynman’s strategy
7:41 - Step 2: example
12:33 - Step 3 of Feynman’s strategy
13:52 - The problem solving procedure
14:23 - Additional tips and tricks
15:51 - Outro
Content
0.08 -> Did you ever find yourself in a
situation during a math or physics class
3.76 -> where you just couldn't understand a single
word coming out of your teacher's mouth?
8 -> Well congratulations, you're human.
It's completely normal to struggle
12.08 -> with understanding some very
complex concepts sometimes.
14.8 -> It's because your teacher is doing a
very bad job at explaining a concept,
17.84 -> but often the concepts are just so complicated
20.24 -> that it's nearly impossible
to immediately understand them
22.88 -> after hearing them for the first time.
24.48 -> In this video, I'm going to show you
a strategy used by Richard Feynman,
28.4 -> one of the greatest physicists of all
times, for solving very complex problems.
32.56 -> I'm also going to show you how
I use this strategy for winning
35.6 -> a medal at the International Physics Olympiad.
37.44 -> Before we get started, make sure to subscribe to
my channel down here for some more tips and tricks
41.52 -> and while you're there you can also hit the
like button to push the YouTube algorithm.
45.12 -> Feynman's strategy can be applied to
almost any kind of problems from simple
48.88 -> mathematics all the way up to differential
geometry and even some business problems.
52.72 -> Feynman was a truly fascinating figure.
55.28 -> He won a Nobel Prize in Physics in 1965
for his work in quantum electrodynamics.
60.08 -> And little fun fact he walked these
very corridors as a student at MIT.
63.68 -> But what made him so special compared to all the
other great scientists was his unique personality
69.2 -> and incredible ability to understand complex
concepts and solve difficult problems.
74 -> Surely Feynman was a very smart guy
76.32 -> but I'm very convinced that his intelligence
alone played only a minor role in his success.
81.2 -> According to himself he only had an
IQ of 124 which means that roughly
86.24 -> five percent of the world population
is actually more intelligent than him.
89.6 -> So if Feynman could revolutionize Physics... this
is kind of weird high gestures... revolutionize...
94.08 -> so if Feynman could revolutionize
Physics with an IQ of 124
98.8 -> just by using clever problem solving strategies,
101.44 -> you can definitely do so much in
your life no matter what your IQ is.
105.2 -> Before I dive into Feynman's
problem solving strategy I
107.84 -> want to show you why having
great problem solving skills
110.48 -> is probably the most useful skill you can
acquire in your entire professional career.
115.04 -> It goes way beyond just solving
math and physics problems.
117.92 -> The reason why some entrepreneurs and
CEOs end up making billions of dollars
121.84 -> is because they managed to solve difficult
problems which others were unable to solve.
126.08 -> So you gotta ask yourself — do you want to
get paid just for the hours you invest like
130.08 -> a factory worker or do you want to get paid for
your unique ability to solve difficult problems?
135.2 -> A factory worker can only make linear
contributions, so if he does a twice as good of
140.158 -> a job he might double the revenue for his company.
Therefore he might get a twice as large salary.
144.96 -> But problem solvers can make
exponential contributions,
148.16 -> so if you become twice as good as solving
problems you might significantly boost your
152.32 -> company's revenue putting almost
no upper bound on your salary.
155.92 -> Therefore, if you want to
become successful in your
158.16 -> career you should become a great problem solver.
160.56 -> Let's have a look at the problem that I made up.
So we can solve it using the finance strategy.
165.28 -> It may be a bit too easy or too hard
for you depending on your math skills,
168.72 -> but try to focus on the solving strategy
rather than on the problem itself.
172.72 -> A drug test is 90 sensitive and 80
specific. Assuming 5 percent of the
178.08 -> total population consumes drugs, is a one-time
random test a good way to identify drug users?
183.92 -> Feynman's problem solving
strategy works roughly as follows.
186.8 -> Step number one is write down the
problem that you want to solve.
190.16 -> Don't just copy it from the textbook, but
try to rewrite it in a way that you can fully
194.32 -> understand it and then try thinking about
what solution you're actually looking for.
198.24 -> For me, during Physics and Math competition
that meant pulling out key information
202.16 -> converting to appropriate units
and defining key terminology.
205.36 -> Don't feel embarrassed to spend
a lot of time analyzing all of
208.08 -> the terminology and understanding
every single word in the problem.
211.12 -> Understanding the problem can sometimes
be the main step in solving the problem.
214.72 -> So once you're confident that you understood
everything the solution might just be obvious
218.96 -> and if it is not obvious then
just move on to step number two.
221.68 -> So let's apply step number one to
our concrete problem. First of all,
225.28 -> what does it mean for a drug
test to be 90 sensitive?
228.64 -> To be honest, I wasn't sure I
had to look it up on Wikipedia.
231.76 -> It means that the true positive rate is 90. Next,
what does 80 specific mean according to Wikipedia?
238.88 -> It means that for 100 people who do not use drugs,
242 -> we will have 80 correctly negative
results and 20 falsely positive results.
247.6 -> If you still struggle to understand this
249.36 -> don't worry. Just have a look at Wikipedia
and the visualization will explain everything.
253.44 -> Five percent of the population
consuming drugs should be pretty clear,
256.48 -> but what does "good" mean in this context.
258.96 -> To understand this, let us think about what would
it mean for a one-time random drug test to be bad.
264.24 -> Bad would probably mean that somebody
who does not consume drugs gets randomly
268 -> tested and the test ends up being positive
270.4 -> meaning that he gets falsely accused
of using drugs even though he doesn't.
273.92 -> So the word "good" in this context
would mean that people rarely get
276.96 -> accused of using drugs even though they don't.
279.2 -> Put in mathematical terms the tests being very
good means that the probability of someone
283.36 -> actually using drugs given that the test came
back positive is very high or close to one.
288.08 -> So if you want to solve the problem
we have to calculate this quantity
291.68 -> and check if it is close to
one. This was step number one.
295.28 -> Instead of just staring at the
problem and thinking about it
297.68 -> forever we already did fifty percent of
the work by just analyzing it carefully.
301.68 -> Step number two according to
Feynman is think really hard and
305.12 -> try to break up the problem into smaller
sub-problems that you're able to solve.
308.72 -> Feynman's thinking process went way beyond
just staring at the problem or a blank wall.
313.28 -> He would walk around, socialize,
talk to his friends and colleagues
316.32 -> and explain everything he knew
about the problems with them.
318.8 -> Feynman was even known for being
a regular guest at a local strip
321.52 -> club close to Caltech where he worked
after completing the Manhattan Project
325.28 -> and he would go there
probably five times per week,
327.52 -> make drawings of naked girls and then he
would also work on physics problems there.
330.96 -> While many researchers talk to
each other about their scientific
333.76 -> research and therefore make a lot of progress,
336 -> Feynman's approach was really
unique because he would talk to
338.4 -> random strangers who had no idea about his field.
341.12 -> Therefore, he had to express everything
in layman's terms in a very simple way
344.88 -> and that helped him a lot
to become a great scientist.
347.28 -> The ideal people to talk to are
curious minds who will constantly
350.24 -> ask the why question, like a little child.
352.48 -> As humans are very curious beings,
354 -> we are constantly trying to figure out
the why behind everything that we see.
357.12 -> One could even argue that this is what makes us
different from all the other animals out there.
360.88 -> If you have to constantly explain all the problems
that you're dealing with in a very simple manner
365.12 -> it will really help you to understand all the gaps
in your knowledge and identify them very quickly.
369.68 -> The most interesting example of a
brilliant idea that Feyman came up
373.04 -> with while explaining a simple concept is
my own field of research quantum computing.
377.44 -> At some point during one of his physics lectures
379.6 -> at Caltech he was explaining why it
was so hard to simulate molecules
383.36 -> and how interesting it would be to use quantum
systems to simulate them more effectively.
387.52 -> This basic idea was the spark which
ignited my entire field of quantum...
392.56 -> This basic idea was the spark which
ignited my entire field of research.
396.56 -> If you would like to know more
about quantum computing and my
398.72 -> PhD thesis you can check out my video over here
401.44 -> where I talk about all the
fundamentals of quantum computing.
404 -> Some of the most difficult concepts that
I ever had to understand in my life were
407.84 -> concepts in quantum mechanics
and quantum electrodynamics.
411.04 -> Coincidentally many of these concepts were
actually initially discovered by Richard Feynman.
414.96 -> The most difficult exam I had in my entire
life was my quantum mechanics final exam.
419.84 -> Luckily I found two good friends who
were roughly as knowledgeable as I am
423.28 -> so we spent the mornings trying to
understand the concepts on our own
426.64 -> and in the afternoon we would come together,
usually without understanding much,
430 -> and try to puzzle everything together until all
of us would understand the difficult concepts.
434.16 -> At later points in my
studies I wasn't lucky enough
436 -> to find someone to study with but it was okay.
438 -> I would just study on my own and
I would try to explain all these
440.4 -> concepts either to my dog Milky
or maybe to some of my plants.
443.92 -> If you are a university student, you could
for example become a teaching assistant.
447.6 -> Just make sure that you will
be actually teaching and not
449.6 -> just spending your time grading quizzes and exams.
451.92 -> I myself volunteered to host the Physics Olympiad
preparations in my home country, Croatia.
456.8 -> This allowed me to rediscover Physics with some of
459.12 -> the smartest and most curious
minds in the entire country.
461.92 -> Back to our drug testing problem. We
know that for a random test to be good,
465.84 -> it means that the probability
of someone actually using drugs
469.84 -> given that the test came back positive
needs to be somewhere close to 1.
474.08 -> Let's have a look at this quantity.
The probability of someone using drugs
478.4 -> given that the test came back positive.
480.64 -> So if this doesn't really look
familiar to you this would be
483.04 -> the point where you would start
talking to friends and colleagues
485.68 -> until somebody would eventually probably tell you
that this looks a lot like the Bayes' theorem.
490.08 -> Obviously, I can't really demonstrate that process
491.92 -> over here, but let's just assume I
got this information from someone.
494.96 -> Feel free to skip to this timestamp for step
497.36 -> number three or just continue
watching. Solve the problem.
500.08 -> So first of all I'm going to start by
writing down the Bayes' theorem in a
503.36 -> way that will be very easy to analyze
and then compare it to quantities.
506.88 -> So let's get started.
513.04 -> So far I haven't really done
anything new. But now when you
515.44 -> look at this you can very easily
see in the first and second line
518.8 -> that A is equivalent to using drugs and B is
just equivalent to the test being positive.
526.24 -> So now that we know what the
quantities mean it should be
528.32 -> very easy to solve the rest of the problem.
537.6 -> All right, so now that we know exactly what
is what. We can just look at the base formula
541.52 -> and try to figure out if we can find what
the quantities on the right side are.
545.28 -> That is, P of B given a P of A and P of B. So
first of all let's start with P of B given A.
554.08 -> But that is just the probability of the test
being positive given that someone is using drugs.
562.8 -> So this quantity is just equal to the sensitivity
that is the true positives which is 90
567.76 -> or 0.1...0.9 and next quantity is just P of A
which is the probability of someone using drugs.
578.4 -> Well we already know that number. That's just five
579.92 -> percent of the people in
total who are using drugs.
582.96 -> The last quantity that we
have to figure out is P of B,
586 -> that is the probability of
the test being positive.
593.04 -> So this may actually be the most tricky part
of this whole problem to figure out because
596.96 -> it's asking us for the probability of a
randomly selected person to be positive.
601.28 -> So if you can't really figure out what a number
would be it's actually quite easy to analyze,
605.12 -> but just imagining a group
of 1,000 people in total.
612.24 -> Out of these 1,000 people, 950 will not
be using drugs and 50 will be using drugs.
622.8 -> Now all that is really left to
do is count how many of these
625.52 -> tests are going to be positive for
each of these two different groups.
628.16 -> So now instead of just looking at
the 1,000 people as a one group
631.44 -> we can just split it up into
950 people who do not use drugs
635.04 -> and there we know how the test behaves
636.96 -> and 50 people who do use drugs and we
also know how the test behaves for them.
640.96 -> So let's first look at the 950 people. We know
that the false positive tests are going to be 20
646.8 -> so we just have to multiply 20 by 950
649.84 -> in order to get how many false
positive tests we're going to have.
657.92 -> So there's a total of 190
false positive tests. For
661.28 -> the 50 people we also know how the test behaves.
664 -> Namely we know that for 90 of the
people who actually do use drugs
667.76 -> the test is going to trigger and is
going to tell us that it's positive.
675.12 -> So all that is now left to do is add up these
numbers. That is 190 plus 45 which is 235.
681.44 -> So we know that out of the 1,000 tests
that we made 235 of them turn positive.
692.64 -> In other words, 23.5 percent of the
tests are positive, so P of B is 0.235.
704.08 -> That is basically it that we have to solve. Now we
706.16 -> just have to plug these numbers back into
Bayes' theorem we are going to get a result
721.84 -> So overall the answer is
roughly 19. In other words,
725.28 -> that means that only four out of five
of the tests are actually correct.
728.88 -> Meaning that for every five people
that get accused of using drugs only
732.56 -> one of them has actually been doing it
and therefore the test is really bad.
736.4 -> This concludes step number two. Just
to summarize step number one was
740.08 -> really understanding the problem
and analyzing every aspect of it
743.28 -> and step number two was talking to other
people and explaining to them everything
747.04 -> you know about the problem so they can
challenge you in everything you say.
750.24 -> Also you should always break down the
problem into sub-problems. Step number three
754.08 -> according to Feynman is write down your solution.
756.88 -> This may sound a bit silly and
I personally haven't written
759.44 -> down many solutions for many
years and I deeply regret it.
762.4 -> As I explained in my video about
the best study methods there are
765.44 -> two parts to learning something
memorization and understanding.
769.36 -> You often make the mistake thinking that
for example Geography your History is all
772.96 -> about memorization and Math and Physics
is just about understanding something
776.64 -> but this is completely wrong.
Understanding a complex concept
779.76 -> may be a great mind exercise but in the
end of the day if you do not remember
783.28 -> what you understood at some point in the past you
will not be able to use that skill in the future.
787.84 -> I personally learned so many advanced
mathematical tools in university and I really
792.16 -> understood them during my exam but then after
the exam I would never really write them down
796.4 -> and nowadays I really regret that I actually
forgot most of them so I can't really use them.
800.32 -> The active recall and space repetition
techniques allow you to memorize things for life.
804.08 -> So after watching this make
sure to check out my video
806.48 -> on space repetition and active recall techniques.
808.72 -> The solution to my struggles which drastically
changed my life in so many ways came from my mom.
814.96 -> One day in 10th grade she came to me and
told me about the software called Anki.
818.96 -> Anki is the only software for which I would
seriously say that it changed my life.
824 -> This concludes step number three. In addition
to Feynman's principles for solving problems,
828.48 -> I'm now going to give you a few tips and
tricks which I use throughout my life.
831.92 -> One of the major reasons why a
lot of people struggle solving
834.64 -> complicated problems especially
if they're under time pressure
837.68 -> is because they don't manage to stay calm and
just follow the problem-solving procedure.
841.44 -> Oh my god okay it's happening everybody
843.84 -> stay calm what's the procedure
everyone what's the procedure.
848.72 -> At the International Physics Olympiad
I would sometimes be confronted with
851.84 -> incredibly complicated problems that
took several pages just to explain.
855.68 -> But instead of panicking and just
staring these problems I would just
858.96 -> calmly follow Feynman's procedure for
solving problems and after some time
862.48 -> I would end up with a solution. If you're still
having difficulty solving certain problems,
866.32 -> at least in mathematics science and maybe
engineering, you can apply the following tricks.
870.32 -> If you struggle solving some kind of
analytical problem or a problem that
873.52 -> has very messy numbers you could for
example replace all of them with one
876.8 -> and try to visualize the entire problem.
Some problems are just too complicated
880.64 -> because they have so many variables so
by setting some of them equal to zero
883.84 -> and solving the problem first you
can understand it and then you can
886.88 -> always come back and solve the original problem.
888.88 -> Or instead of making variables equal to
zero you can simply remove some of the
892.88 -> information from the problem and then
write it down in a more simple way.
896.16 -> If you don't know how to approach
a certain problem maybe you solved
898.88 -> a similar problem in the past so first
have a look at that figure out how you
902.72 -> solve that and then maybe the
solution will become obvious.
905.12 -> Jeff Bezos once wanted to
become a theoretical physicist.
907.76 -> That's why he was studying at Princeton and when
he was really stuck with a problem for many hours,
911.84 -> he then just walked up to a friend and was
like hey I don't really know how to solve
914.88 -> that can you help me and his friend just looked
916.96 -> at the problem he could tell
him the solution on the spot.
919.28 -> When Bezos asked him how exactly he
did that his friend simply replied oh
923.04 -> yeah it's a bit similar to another
problem that he saw in class and
925.84 -> therefore the solution was obvious and Jeff
Bezos was so discouraged by the fact that
929.76 -> he simply couldn't comprehend
this that eventually he gave up
932.48 -> on doing Physics he started Amazon. Also if your
first attempt to solve a problem didn't work
937.76 -> don't try again the same way
try thinking about other ways
940.56 -> you could approach this problem. Quantum mechanics
itself was probably the silliest possible solution
945.44 -> to explain all the inconsistencies
in Physics in the early 20th century
949.04 -> but yet it turned out to be true. These were my
951.28 -> strategies for understanding
and solving complex problems.
954.4 -> If you want to learn more
about how to understand math
956.48 -> intuitively you can check out my video over here.
958.88 -> If you would like to learn about study methods and
960.8 -> memorization methods you can
check out my video over here.
963.36 -> And if you're just curious about my PhD
research in Quantum Artificial Intelligence
967.44 -> check out my video over here.
968.72 -> Thanks for watching don't forget
to like the video and subscribe to
971.52 -> my channel and I'll see you next time. Take care.
Source: https://www.youtube.com/watch?v=yoFBiyg_ulg