Art of Problem Solving: Counting Paths on a Grid

Art of Problem Solving's Richard Rusczyk explains how to count the number of paths from one point to another on a grid.

[shaswatsingh]

You've earned yourself a subscriber. And that last joke earned you the like. :)

[yeojunjeon]

"EENNEWEENE is one word that is worth almost a thousand pictures."
- Richard Rusczyk, 2012

[KAMFlamenco]

This video really helped me understand the Lattice Path problem. Many thanks!!

[zelo_s]

Ok, So when does a Hot Dog Stand Turn Into Thai Food?? You'll understand in he beginning of the video

[Dkdkxncnchz]

can't believe this man literally finished the 30min class in 8:47

[SamvitAgarwal]

Is there a way to do this if some of the squares are blocked(you cant cross them)?

[cavetivitic]

These Study Pug ads be annoying while I watch this vid:/

[kaustavMM]

This helped a lot. They didn't teach this in combinatorics

[pcalde]

Wow, thank you very much, I was really struggling on why it was this way and you really nailed the explanation

[MrPeacelovejustice]

"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.

[haleywelliver]

"like most guys, i navigate by gut."

[efebora]

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)?

[michaelempeigne]

very simple method.  I like it when it looks simple and explanation included.

[stsfoxfacel]

Like for "one word that's worth almost a thousand pictures" :D

[tameemsani]

great you look like jimmy from better call saul

[pukumar]

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?

[mohamedatti]

How to calculate the number of rows of Arrays in PV plant of a non uniforme shape

[johnnywong]

May I know if this topic is covered in PreAlgebra text book by Aops

[shinsena]

you should have done an irregular shaped polygon for that

[uwuslayer]

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?