# The problem in Good Will Hunting – Numberphile

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 higher you go up in math the more nonsense you get

What's the name of the song @Numberphile / @AlanKey86 ? I try to look on the channel but I didn't find at all!!!

This is al human knowledge, maybe we are al wrong about the calculations.

Matt Damon is an amazing actor. To think that that man passed himself off as a genius, incredible performance.

You put a banned over a non banned bit

Dam, lead singer for Radiohead can throw down some math skills.

I did this myself and I managed to find all 9

Please can you solve the Oxford street pickpocket problem?

Irreducible @ 2:30 it is banned because nothing interesting. Lol, needs further explanation.

Pale red haired maths nerd is just my type.

take care of your self bro you are like dieing

You're still Lumbered, England's Rose.

I saw the pigeons in background

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.

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 🙂

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 🙂

There are actually 13 ways to solve this.FYI google says Matt Damon is 5'10"

love this.

i love the wallpaper

Math Damon

3:15 he just pulled a ''this problem is trivial and left as an exercise to the reader''

okay but now give the prufer encodings

Those MIT professors are now janitors

It takes me longer than 2 years to put shelves up. Not because it is hard, just because.

Oh damn I did this in 5 minutes !!!!!!

Wtf is this

Thank you, I am so doing this with my AP physics class!

Hey but isn't this similar to how carbon chains look like?

I've been wondering about this.

Did I see you in another video demonstrating the Razzle Dazzle game?

The poblem

Russell wrote a book.

"Hold my beer"

-Gödel

Why the first one have a space in it?

P = P

Connective law inbicious daemon.

Just isomers lol

Wha- no! That's what he second math problem that he said was way easier! We never know the first problem

10 Selfifot 😋👁

That's number Wang!

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.

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.

this was actually really easy

Awwww your pigeon wall behind you is soooo cute!!❤

The banned is bs , otherwise every person could do it.

Sees thumbnailLet me guess… Optimal stopping theory?This is just alkanes and alkenes

My favourite movie after The Breakfast Club

I heard it was originally suppose to be a sassy troubled wedding planner, and it was called Goodwill Bunting!

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.

Interesting Video , I must subscribe

Actually that's a Feynman diagram without the proper squiggly line

The end is a lie. I am the teacher. It never happened

I honestly was able to draw all 10 of those trees. Took me a day though. How long did it take you all?

Can't watch shakycam, sorry.

It's all your fault

He lost me at tree's.

Alter, ist der britisch!

omg it organic chemi

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).

well, this looks easy… am I a genius now?

I remember that old mechanical calculator behind him. Today's students would crack up if they saw it multiply and divide.

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.

How can you prove that there are only 10?

I thought this was actually a difficult problem until i realized it’s just basically isomers

B(

Math! It's just Math!

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

10 or 11 trees 🤔 !

How did the guy in the film, the janitor, understand the rules?

The same question was on my GED LOL

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.

Matt Damon is, ESTUPIDO!

His talking about the late prof emiritas stephen hawking

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.

It's way cooler when Matt Damon solves it

you drew a few there that were wrong by you're own explanation.

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.

Crushed it… so simple

that's it ??? so waht's the problem ?

I hate him

Here is a question: does math refer to reality?

Draw all of TREE3

poblem.

omg i've been waiting for this … :DD and now that I have seen it I am even more fascinated because this was a problem I have once considered… how many distinct trees there are on n vertices

Creepy smiles.

Is it just me or anyone found all the 10 tree in 10 minutes.

The best part of the story is that the actual person was a student at UC Berkeley. Go Bears.

It took me only like 5 minutes to find out all 10 trees and I don't know the answer, that makes me think that drawing is not the hardest part. The real question is how do you know there are only 10.

The student when was late that solved the unsolvable problem was Stephen Hawkins

That explains a lot. I think my math tests at school were full of unsolvable problems xD

The solution is correct, but you failed to show your work. C-

Oh i actually got all of them right in about 4 Minutes. Am i now smarter than mit prof?

I did the rest. So, am I "wicked smart" worthy?

His upper lip freak me the fok out. Great video tho

"It might sound greek to you."

But i am greekHomoerotical trees

I found the film nowhere not in netflix not in prime video

Please Can any suggest where I can find it …

So the real problem here was the statement

Hi Numberphile, how are you and what did you have for breakfast today?