Art of Problem Solving: Counting Paths on a Grid
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- čas přidán 27. 12. 2011
- Art of Problem Solving's Richard Rusczyk explains how to count the number of paths from one point to another on a grid.
Learn more problem solving techniques at our site: bit.ly/ArtofProblemSolving
"EENNEWEENE is one word that is worth almost a thousand pictures."
- Richard Rusczyk, 2012
You've earned yourself a subscriber. And that last joke earned you the like. :)
This video really helped me understand the Lattice Path problem. Many thanks!!
the one from project euler?
Wow, thank you very much, I was really struggling on why it was this way and you really nailed the explanation
Very useful and nicely explained! 😃👍
Neatly done!
Amazing!!:) Really helpful! Thx!
Great video!!!
Thanks! This was so helpful!
v skcjdniajeicuruwif
extremely useful video
pure gold !
Splendid! Thank you
great explanation!! thank you so much!
thank you so much it helps me a lot .
Can i ask how to count the amount of turns on a grid if its m by n and m is always bigger then m, what formula?
very simple method. I like it when it looks simple and explanation included.
thank you
This man is a genius
Ok, So when does a Hot Dog Stand Turn Into Thai Food?? You'll understand in he beginning of the video
ikr
XDD Lmao imagine how i laughed when i realises wut u mean. Take my like bro
@@hamburger6665 I honestly don't remember this comment lmao
@@zelo_s6707 XDD
@@hamburger6665 I also can't seem to remember the joke, please enlighten me
This helped a lot. They didn't teach this in combinatorics
Is there a way to do this if some of the squares are blocked(you cant cross them)?
yes
@@srsingh888 how should this be done - when some squares are blocked? can you explain?
@@haiyang1000 welp same quesion
although I breaked the quesion with brutal force (counting)
hamburger 666 😂😂
@@memecage7029 well counting works so i dont care XDDD
Thank you
Awosome man really love it 😘😘😘
May I know if this topic is covered in PreAlgebra text book by Aops
Intro to counting and propability
thanks :)
thank you :')
Great explanation, thanks for posting. In the first part of the problem, are the number of paths counted to get to the destination in the shortest way, or are they all possible combinations? A traveler could also go N-E-S-E-N-E-S-E-N-E? Could you please advise?
There are an infinite number of paths if you don't set any parameters. For example, you can walk in a circle a hundred times then continue to your destination. This problem is counting the number of shortest paths.
can't believe this man literally finished the 30min class in 8:47
nice sir .
u are a genius!
you should have done an irregular shaped polygon for that
"like most guys, i navigate by gut."
But u are not a guy
Pro Da how do you know
@@wojak6793 cuz she has a feminine name and a girl profile picture
great explanation......btw you look like jimmy from better call saul
Astounding pedagogy.
Plz can anyone tell me that how can I find the path number in a grid has obstacles(which can block some path)
did you figure it out
Cheers, Linus
Like for "one word that's worth almost a thousand pictures" :D
so how do u find the total no of paths? one step west is just one possibility, he could have taken 4 steps west or maybe 2 steps south and 2 west? Then how will you find the total no of paths? Should we just consider it to be infinity or can we calculate it?
If you are allowed to take as many west steps as possible, then there is nothing to keep you moving towards the destination. So you're right, it would be infinite as you could easily just circle (square really) back and forth.
How to calculate the number of rows of Arrays in PV plant of a non uniforme shape
If we were looking at a 10x10 grid, how many paths could be taken if we could only go up and right (north and east)?
So 10x10 grid means we have to take 20 steps.
Of these 20 steps 10 need to be north and 10 need to be east.
So choose any direction, I choose north in this case, and find the nCr.
So, 20C10 = 184756
Omkarz Thank you so much!
oh also let’s say that we draw a diagonal line thru the 10x10 grid, how would we find the all paths that don’t cross above the diagonal? so basically we can only go up or right again however this time the order matters because we can’t go above the diagonal line cutting the 10x10 in half. Our professor asked this question as a bonus credit and I realized that everyone in class was struggling so I’m just hoping to find an answer for it somewhere. Thank you again for your time
@@efebora2000 I think the answer would be half of the answer without the diagonal which is 92378.
I currently don't have a pen and paper with me to work out the math, I will post a definitive answer later.
Edit: It is definitely not just half, it is a lot less than that
Omkarz I thought about that too but this time the order matters so I think we might need to use permutation (nPr) instead of combination (nCr). Thank you for your time, I just need to find an answer before 8am tmrw I’ll also try my best to work it out. Thanks for the help
thanks
nice!
This has great YTP potential
Great Explanation !!! ;)
legend
"Like most guys, I navigate by gut" 0:55
a gut full of hot dogs, egg sandwiches, Indian food, and fantastic Thai food from another hot dog stand.
Seems like the gut directs men directly to food.
so true
How do you compute the number of ways if there is way to move diagonally upwards, towards the right?
Did you find the answer for this? I'd like to know.
how you get number 9 in second grid ?
Kuldeep Singh after you make a step west there are only 9 steps left
gotta make the intro song my new playlist
i subscribed 1 minute into the video
nice vidio
I giggled at every Eenneweene
So I was doing some Coderbyte challenges and a problem similar to this came up... spent hours figuring it out myself, came up with some tidbits of the solution but never quite made it. So I gave up and looked at other people's solution which confused the fuck out of me. Thanks to this video I feel a little less dumb now
what about 3D? how can we calculate it?
You have three choices to make +x +y and -z, then same procedure.
you a G
WOw.Good
I was going to say hey you can't take the first step west then i realised the starting point wasn't at the corner!
Luv
Is his compass right? I get what he’s saying it’s just kinda throwing me off
eeneeweenie lol
weene
@@dpquesties2513 kik
These Study Pug ads be annoying while I watch this vid:/
Eenneweene which actully mean east, west, north,rather than ________
Ahahha dude great explanation also really funny
GRE anyone?
Watch me whip,watch me 1.50
You eat two hot dogs and one egg sandwich on the way to work? Why no breakfast
What about souths!!
We are taking the scenario in which you can only move north or east. If we were able to move south, we could have infintite solutions.
8 steps? That's a 3x5 grid... don't we have a maximum of 15 steps we can take? Why do we only consider 8 steps (and then 9)?
We can only move right and up.
3x5 covers all movements. Which is not asked.
This person is very Hungry.
Neeneene
Maram tata n
NO WAY THIS GUY ACTUALLY NAVIGATES BY GUT
THATS WHAT I WAS THINKING
SAME
i liked your, RAAAOUT !!
E E N N E W E E N E
art of problem solving
He looks like he stucked in 2002 Math Class
bruh....
Why take (8/3(North)) and not (8/5(East))
8/3=8/5
Jhatu kya bta rha h
too complicated
Jai Vasandani it was simple
just a suggestion
make your videos more simple.....thanks
its simple
Bruh get to hte point ffs