DR. JAMES GRIME: Yeah, but like
all mathematicians, he’s tall, blond, and handsome. Yeah? Yeah? -Well, he’s not tall
or blond or– is he? DR. JAMES GRIME: Yeah. -Is he? He’s not tall. DR. JAMES GRIME: I don’t know. I wasn’t counting. I guess the choice of
maths was arbitrary. They wanted to do a film about
a troubled genius. And originally they were going
to do physics genius. And then they were advised to
pick a mathematical genius because it might work better
with the script. It’s a really good film. And the maths is
less important. Should we talk about what they
did in the film, the maths? -Yeah. DR. JAMES GRIME: All right, so
we’ll talk about that first. Near the beginning of the film,
the MIT professor sets his students a challenge. Who can solve this? I put it on the blackboard in
the corridor, and who can solve this problem? And it’s taken MIT professors
two years to solve this problem. Can you do it? Now, is it as hard
as he made out? So what was the problem? If I say it first of all– I’m going to say the problem
that he gave the students. It might sound like Greek
to you, because some of it is Greek. Right so then I’ll
say the problem. Then I’ll tell you
how it works. And it’s a problem we
can all do at home. I promise. So the problem is, draw all
homeomorphically irreducible trees of size n equals 10. What does that mean? All right, let’s try this out. These things are called trees. So I have trees. Instead of that, they are
networks of dots and lines. So these are called graphs. It’s like the London
Underground map. So a network of dots
and lines. So this is called a tree. And what’s not allowed,
what is banned is something like this. This is banned. This has a cycle in it,
and cycles are banned. Now what was that other
big word I said? Homeomorphically. That’s the worst one. That’s actually not so bad. That means if I did
this, these two are the same picture. Can you see what I’ve done. I’ve just moved the
dots slightly. So you can rotate them
and reflect them. Or you could move them
around slightly. But those two pictures would
count as the same thing. And there was another
clever word. There was the word irreducible
in there. So that’s another
banned thing. Here this time what is banned
is something like this. This is banned. Only two lines go
into that dot. Which means pretty much
nothing happens. You go in and you
go out again. Nothing happens. There’s no change. Nothing interesting here. So this is banned as well. Those are the rules. We want to do it for 10 dots. This is the problem
Will Hunting had. 10 dots, how many ways
are there to do it? I can tell you, there are
10 ways to do it. What I thought might be fun is
if I did a couple of them, and maybe leave some for people
to try and work out what I’ve left. No? -I want to see all of them. DR. JAMES GRIME: You want
to see all of them? All right. So the first one is. So it’s there. So if you can do that in less
than two years, then you’re better apparently than
MIT professors. Or if you prefer, these are
all the trees of size 10. Or this is a spider with nine
legs and that’s a guy with a funky Afro. I don’t think that’s
a particularly– I think people can
do this at home. But the problem isn’t
the important thing. What I really would like to talk
about is who was the real good Will Hunting. The story is, well– so Will Hunting solves
this problem. There is an urban legend that’s
similar of a student who ran into his exam late. And he copied down the problems
from the board. And he went and solved them. And the last one seemed
really hard. But he kept working on it. And he managed to solve it. And he handed in
his exam paper. And then the professor rings
him that night saying, you were only meant to do the
first few problems. The last one was an unsolvable
problem. Ah, you solved it.

The problem in Good Will Hunting – Numberphile
Tagged on:                         

100 thoughts on “The problem in Good Will Hunting – Numberphile

  • March 5, 2019 at 3:45 pm
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    You look so much like Brick Top!!! it took me a few years to realise. There was always something familiar in your appearence.

    Reply
  • March 11, 2019 at 1:35 am
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    And what is the purpose of this

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  • March 12, 2019 at 10:23 pm
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    Who is the person behind the camera? I swear I know him.

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  • March 13, 2019 at 1:57 am
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    I decided watched this movie today and I loved it. Could've focused a little more on the maths, but whatever, that's why we have you, James! A weird thing though is the title of the movie, which made me initially think it was a movie about hunting. Luckily I saw your videos, otherwise I might never have watched the movie!

    Reply
  • March 14, 2019 at 2:36 am
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    Ok, now prove that you've found all the possibilities using probability theory, and without assuming that there are only 10 options. Then write a script in Python that can solve the problem by itself.

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  • March 17, 2019 at 6:40 am
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    There is an 11th and 12. There are at least 2 more. 2nd column, 3rd row. 2-2-3, and 1st column 2nd row, 3-2-3 and 3-3-2

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  • March 17, 2019 at 5:13 pm
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    But where’s the proof?

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  • March 18, 2019 at 11:28 am
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    Not a urban legend. Student was from the University of Zambia. Solved the unsolved problem. No info on him or that problem on YouTube. And I don't know more details.

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  • March 18, 2019 at 3:13 pm
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    Math Demon

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  • March 19, 2019 at 6:10 pm
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    I feel like you oversimplified the problem by telling us that there were 10 solutions. I agree that given this information anyone could solve the problem. I haven’t seen the movie but I can’t imagine the professor gave his students the same information making the hard part not just coming up with the solutions but rather knowing that those 10 solutions are the only possible 10.

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  • March 20, 2019 at 2:47 pm
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    Found a real life hobbit

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  • March 21, 2019 at 2:06 am
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    … actually the tree problem was NOT the first problem the professor gave in the film. He gave the tree problem after the first problem was solved so quickly and he couldn't find the math wiz. That's when professor said….. "we've put another problem that took us two whole years to prove….. the faculty have answered and answered with vigor."

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  • March 22, 2019 at 9:26 am
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    Why isn’t the spikey ball banned? According to the rules

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  • March 22, 2019 at 7:20 pm
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    Anyone else tried to solve the problem by classifying trees based on the maximum degree of any vertex?

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  • March 23, 2019 at 3:29 am
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    Yeah. Once you understand the rules, it’s just a puzzle. That’s not that hard. Well it could be hard since you are asked how many solutions are there instead of, find the 10 solutions. When you don’t know the finish line, it can get hard to think of the last solutions because your brain will keep repeating the ones you’ve already solved. But it’s easy to understand what to do

    As a 3D digital artist, I see a huge game of connect the dots every day. Lol. I also think of mother boards. So yeah, it’s not math, it’s a game. Lol

    Reply
  • March 27, 2019 at 1:32 am
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    here is a little fun thing to do, once you understood the rules, pause the video, try it out and find your draw between the ten trees.

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  • March 29, 2019 at 10:24 pm
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    This ginger boy is smart

    Reply
  • March 30, 2019 at 2:29 am
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    Pigeons

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  • April 3, 2019 at 9:55 am
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    the higher you go up in math the more nonsense you get

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  • April 4, 2019 at 6:04 pm
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    What's the name of the song @Numberphile / @AlanKey86 ? I try to look on the channel but I didn't find at all!!!

    Reply
  • April 7, 2019 at 1:56 pm
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    This is al human knowledge, maybe we are al wrong about the calculations.

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  • April 10, 2019 at 8:37 pm
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    Matt Damon is an amazing actor. To think that that man passed himself off as a genius, incredible performance.

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  • April 11, 2019 at 4:47 pm
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    You put a banned over a non banned bit

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  • April 11, 2019 at 9:40 pm
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    Dam, lead singer for Radiohead can throw down some math skills.

    Reply
  • April 13, 2019 at 2:57 pm
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    I did this myself and I managed to find all 9

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  • April 13, 2019 at 8:07 pm
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    Please can you solve the Oxford street pickpocket problem?

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  • April 16, 2019 at 6:59 am
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    Irreducible @ 2:30 it is banned because nothing interesting. Lol, needs further explanation.

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  • April 18, 2019 at 2:30 am
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    Pale red haired maths nerd is just my type.

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  • April 18, 2019 at 3:51 pm
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    take care of your self bro you are like dieing

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  • April 18, 2019 at 7:20 pm
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    You're still Lumbered, England's Rose.

    Reply
  • April 20, 2019 at 2:34 pm
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    I saw the pigeons in background

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  • April 21, 2019 at 2:16 am
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    I paused the video at 3:06. It took me 3 minutes to do the first 10, then another 2 minutes to persuade myself that there was no other nonidentical trees that can be made.

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  • April 21, 2019 at 2:24 am
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    I paused the video at @. It took me 3 minutes to do the first 10, then another 2 minutes to persuade myself that there was no other nonidentical tree that could be made. And I sell air conditioning systems smh 🙂

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  • April 21, 2019 at 2:24 am
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    I paused the video at @. It took me 3 minutes to do the first 10, then another 2 minutes to persuade myself that there was no other nonidentical tree that could be made. And I sell air conditioning systems smh 🙂

    Reply
  • April 21, 2019 at 4:13 am
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    There are actually 13 ways to solve this.

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  • April 21, 2019 at 4:16 am
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    FYI google says Matt Damon is 5'10"

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  • April 21, 2019 at 9:37 pm
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    love this.

    Reply
  • April 22, 2019 at 2:58 pm
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    i love the wallpaper

    Reply
  • April 23, 2019 at 5:38 pm
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    Math Damon

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  • April 24, 2019 at 3:46 am
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    3:15 he just pulled a ''this problem is trivial and left as an exercise to the reader''

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  • April 24, 2019 at 11:37 pm
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    okay but now give the prufer encodings

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  • April 27, 2019 at 7:51 pm
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    Those MIT professors are now janitors

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  • April 27, 2019 at 10:41 pm
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    It takes me longer than 2 years to put shelves up. Not because it is hard, just because.

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  • April 28, 2019 at 3:40 pm
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    Oh damn I did this in 5 minutes !!!!!!

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  • April 29, 2019 at 2:05 pm
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    Wtf is this

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  • May 4, 2019 at 8:24 pm
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    Thank you, I am so doing this with my AP physics class!

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  • May 7, 2019 at 9:07 pm
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    Hey but isn't this similar to how carbon chains look like?

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  • May 8, 2019 at 1:25 am
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    I've been wondering about this.

    Reply
  • May 8, 2019 at 6:45 pm
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    Did I see you in another video demonstrating the Razzle Dazzle game?

    Reply
  • May 9, 2019 at 10:33 pm
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    The poblem

    Reply
  • May 18, 2019 at 3:31 am
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    Russell wrote a book.

    "Hold my beer"

    -Gödel

    Reply
  • May 20, 2019 at 12:27 am
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    Why the first one have a space in it?

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  • May 22, 2019 at 8:07 pm
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    Connective law inbicious daemon.

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  • May 26, 2019 at 10:57 am
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    Just isomers lol

    Reply
  • May 28, 2019 at 6:01 am
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    Wha- no! That's what he second math problem that he said was way easier! We never know the first problem

    Reply
  • June 7, 2019 at 12:09 pm
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    10 Selfifot 😋👁

    Reply
  • June 7, 2019 at 8:18 pm
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    That's number Wang!

    Reply
  • June 8, 2019 at 9:33 pm
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    I don't see the big deal. The problem seems solvable to me, as a high school student. I solved it in like two days of work.

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  • June 9, 2019 at 10:50 am
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    I feel like in order for the solution to be complete, we shouls also prove that there are no other trees than the ones drawn. And that's not so trivial.

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  • June 11, 2019 at 2:21 pm
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    this was actually really easy

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  • June 12, 2019 at 4:16 pm
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    Awwww your pigeon wall behind you is soooo cute!!❤

    Reply
  • June 12, 2019 at 8:52 pm
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    The banned is bs , otherwise every person could do it.

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  • June 14, 2019 at 9:45 pm
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    Sees thumbnail Let me guess… Optimal stopping theory?

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  • June 16, 2019 at 2:05 pm
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    This is just alkanes and alkenes

    Reply
  • June 20, 2019 at 5:21 pm
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    My favourite movie after The Breakfast Club

    Reply
  • June 25, 2019 at 6:56 am
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    I heard it was originally suppose to be a sassy troubled wedding planner, and it was called Goodwill Bunting!

    Reply
  • June 25, 2019 at 8:09 pm
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    I don’t get why everyone is saying that this problem is so easy. I got a 760 out of 800 on the SAT in math (top percentile). I have also passed the AP calculus AB test with a score of 4 (not great, but still better than the majority of students that take the test). I have also gotten an A in my college calculus course, but I could not draw those diagrams. I don’t really understand the problem to be honest. I am willing to bet that most people could not actually draw all of the trees so easily.

    Reply
  • June 26, 2019 at 12:19 pm
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    Interesting Video , I must subscribe

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  • June 28, 2019 at 11:40 am
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    Actually that's a Feynman diagram without the proper squiggly line

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  • July 1, 2019 at 12:11 am
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    The end is a lie. I am the teacher. It never happened

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  • July 1, 2019 at 5:29 pm
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    I honestly was able to draw all 10 of those trees. Took me a day though. How long did it take you all?

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  • July 2, 2019 at 9:59 am
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    Can't watch shakycam, sorry.

    Reply
  • July 13, 2019 at 12:53 am
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    It's all your fault

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  • July 13, 2019 at 4:33 am
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    He lost me at tree's.

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  • July 16, 2019 at 8:30 pm
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    Alter, ist der britisch!

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  • July 18, 2019 at 8:45 am
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    omg it organic chemi

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  • July 18, 2019 at 3:48 pm
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    As a competitive programmer this is how I understood the problem. Construct all trees such that there are 10 vertices, and no vertex with a degree of 2. A tree can only be considered different from another if there is at least one difference in the degree of a vertex. (Note: In graph theory, tree implies that there are no cycles).

    Reply
  • July 19, 2019 at 11:59 pm
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    well, this looks easy… am I a genius now?

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  • July 27, 2019 at 2:19 am
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    I remember that old mechanical calculator behind him. Today's students would crack up if they saw it multiply and divide.

    Reply
  • July 30, 2019 at 6:05 am
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    Srinivas Ramanajun was the real person that the story was based on, he was referenced in the movie. Dev Patel played him in a movie. Looked nothing like him, but at least his story was told.

    Reply
  • July 31, 2019 at 1:20 pm
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    How can you prove that there are only 10?

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  • July 31, 2019 at 10:48 pm
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    I thought this was actually a difficult problem until i realized it’s just basically isomers

    Reply
  • August 3, 2019 at 2:13 am
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    Math! It's just Math!

    Reply
  • August 3, 2019 at 5:26 am
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    pretty sure this is on the same level as basic organic chemistry homework that can be done in a week so i guess I am better than MIT professors

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  • August 4, 2019 at 8:53 am
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    10 or 11 trees 🤔 !

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  • August 6, 2019 at 2:38 pm
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    How did the guy in the film, the janitor, understand the rules?

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  • August 10, 2019 at 4:09 pm
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    The same question was on my GED LOL

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  • August 11, 2019 at 4:57 pm
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    The way you did it was hard, as in it was random. There's easy & systematic approach to the problem which can be used for even more dots. It makes everything easier to keep track on & figure out the next diagram.

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  • August 13, 2019 at 4:20 am
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    Matt Damon is, ESTUPIDO!

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  • August 13, 2019 at 9:38 pm
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    His talking about the late prof emiritas stephen hawking

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  • August 14, 2019 at 5:47 am
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    I disliked the film. Matt Damon had the personality and acting skills of a cardboard box. Didn't warm to the character at all. Robin Williams briefly threatened to make it almost interesting, but I wouldn't watch it again.

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  • August 14, 2019 at 2:06 pm
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    It's way cooler when Matt Damon solves it

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  • August 15, 2019 at 9:31 pm
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    you drew a few there that were wrong by you're own explanation.

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  • August 22, 2019 at 5:03 pm
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    Solving this problem by hand for n=10 is doable. But what if n can have any positive integer value? Is there a formula that gives the number of different trees for any n (with a proof of course)?
    That should have been the real problem in the movie.
    Maybe that's impossible to solve idk, let's give a try.

    Reply
  • August 23, 2019 at 10:41 am
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    Crushed it… so simple

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  • August 25, 2019 at 9:00 pm
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    that's it ??? so waht's the problem ?

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  • August 28, 2019 at 11:44 am
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    I hate him

    Reply
  • August 29, 2019 at 3:09 am
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    Here is a question: does math refer to reality?

    Reply

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