3-D Path Counting Brain Teaser

Extending the path counting to three dimensions

Category:

Education

Tags:

• brain
• teaser
• trinomial
• path
• counting
• dimension

[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.

[TheLittleMan123]

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

[midnight4fox]

what program is he using?

[basalisk335]

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

[howtomakewallets]

l f2 rubiks cube talk



[supersushi269]

You could have used a 3d software like blender

[happyguyrulz]

what if you go in an 'S' Shape?

[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.

[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.

[helpee]

more brain teasers!!

[athleticallan321]

I was wondering, did you use paint for this?