3-D Path Counting Brain Teaser

[howtomakewallets]

l f2 rubiks cube talk

[TheLittleMan123]

i was bored and figured out that with a 5x5x5 cube, with this principle, it would be 23100 ways to go =)

[basalisk335]

@TheLittleMan123 i think it's 34650 ways actually, 12!/(4!^3)=34650

[supersushi269]

You could have used a 3d software like blender

[happyguyrulz]

what if you go in an 'S' Shape?

[helpee]

more brain teasers!!

[athleticallan321]

I was wondering, did you use paint for this?

[FranchiseIndustries]

@athleticallan321

I think he uses SmoothDraw. Not only that, As a drawing tool, he uses one of them bamboo pens, at least in the later versions where his writing is a bit more neat.

[kinovers4]

6C2 + 4C2

[yubjuli]

it is more interesting if you imagine there are cells inside the cube

[FireWallBurns]

Really must teach simple math? Skip the damn _+_=_ thing! Just say the ways to get there

[hctivas]

use dynamic programming or recursion.

[TheStandish13]

What program is this??

[rocco133]

you mean paint?!

[hifhif123]

Why would lawyers need this sort of thing

[DatRichColombian]

i feel like poindexter from revenge of the nerds.........ITS GREAT ^.^!!! I ACTUALLY UNDERSTAND THIS!!!!!!!!! could be the fact that i no how to solve a rubix cube...

[spider853]

sorry but I didn't understand the (x+y+z)^n part...

in this cube what is n and what is x,y,z ?

[laputahayom]

have you watched the one before this?

[spider853]

Yes.. sorry I've understand after watching it one more time.

[thekkl]

x, y, and z are the three dimensions. I don't know what n is cause I don't really understand it either =\

[konopong]

I like to think of solving these type of problems in terms of permutations with indistinguishable elements. So here to get to the opposite corner of the cube you need to make 6 moves, 2 to the right , 2 to the left and 2 moves down. You could also think in terms of the x,y,z directions. So, anyway, So how many permutations are there of RRLLDD? There are 6!/(2! 2! 2!) which equals 90.

[laputahayom]

that a good way to work it out

[Pelerouchi]

@konopong That can be generalized to a n-dimensional hypercube where you can take m steps towards each direction. That gives you (m + m + ... + m)! / (m!*m!* ... *m!) = (mn)! / (m!)^n permutations. To fully understand why you need to understand multinomial coefficients. Sadly they have a tendency to fuck ones brain out...

[Mozza314]

@konopong You can also use this idea to extend to an arbitrary number of dimensions. So if I have n dimensions and a side length of s, I need to make s-1 movements in each dimension (e.g. with our example we move 2 right, 2 left and 2 down), and so we have n*(s-1) steps and we get [n*(s-1)]! / [(s-1)!^n]. So in Sal's previous problem n=2, s=6 we have [2*5]! / [5!^2] = 10! / (5! * 5!) = 252. In this one we have n=3, s=3 and we get [3*2]! / [2!^3] = 6! / (2! 2! 2!) = 90.

[elitesuperhaxor]

good example of pascals triangle

[btkw]

nice

[Sciesch]

Cool video, gotta watch it again I'm in a hurry right now :)

[MustNotRead]

i think i actually have a 2D brain inside my skull, so this was impossible for me. :(

[abhir314]

Excellent! :-)

[Pootboot]

fghd