Legendary Pokémon

He's Hugh Laurie.










OMFG, that smile.

Haha, I told him we've got Hugh Laurie fans here...

Anyway. That should be a hard one.


Let's see the dimensions along with their corresponding shapes:
1D - Line segment
2D - Square
3D - Cube
And so on...
As we can see, every time you add a dimension, you get a different shape. Each of those shapes has a different number of points (also known as vertices), edges, faces and so on. They're called the elements of the shape. Below is a diagram that shows the number of points and edges for 1, 2 and 3 dimensions, the ones that can actually be drawn:


(Blue numbers indicate the points, red ones indicate the edges.)

Now, assume we keep adding dimensions till we end up with a 12D shape. Your job is to tell me how many edges has this 12D shape.

Tip: You have to think about how each shape is generated. Work with what you have, the 3 first dimensions.

Enjoy.

The 12D shape must have 4096 edges.

Nope.

By the way, edges = ακμές in greek.

There are 24576 edges, and I have a mathematical method to my madness to back it up.

The number is correct, good. But post your method if you want, there are more than one ways to prove it, I just wanna see if we used the same one.

Okay, my mathematical madness:

As you went up a dimension, the vertices doubled each time. Therefore, The twelfth dimension would have 4096 vertices.

Also as you went up a dimension, the number of segments each vertex touched increased by one. So in the first dimension, each vertex touched one line. In the second dimension, each vertex touches two segments, in the third dimension, 3, and so on and so forth.

Now all I needed to find was a formula that used those two variables and would give me the number of edges. The formula is:

Edges= 1/2 vertices * dimension number

You can try it with the first through third dimension shapes, and it works. Therefore, I inserted the twelfth dimension numbers in and:

Edges= 1/2 * 4096 * 12
Edges= 24576

Nice one! The logic is the same as the one of the formulas I used pretty much, though the actual formulas are different. I began by thinking how each of the elements is generated by moving forward one dimension. You basically double any elements you had in the previous shape, plus, "extend" them. By extending them, I mean that every vertex becomes an edge, every edge becomes a face, every face becomes a cell, etc.

So, if x is the number of dimensions, V is the number of vertices, E for edges, F for faces and so on, I ended up with the following formulas:

V(x) = 2^x
E(x) = 2*E(x-1) + V(x-1)
F(x) = 2*F(x-1) + E(x-1)
...and so on...

But yeah, your thing is much faster as you don't have to calculate the edges of each dimension. Kudos to you man, glad to see another math freak in here.

wow he deserves the goutis badge after the redisign of lp

*hint, hint* we get badges at redising

Want teh moar challenges.

what is 12d??????????????????

12D= 12 Dimensions. Next Challenge NM2!

I had definitely not forgotten of this thread! So, there we go:


您应该查寻烟肉暗号。
↓
BABAABAABAAABAAAAAAAAAABAAAAAAAABAABAABAAAAAABAAABAAABAABAAAABBBBAABBBAABAABAAAB​BABBAABAAABAABBAABBBAAAAABAABAAABBBABAAAAABABBAABBABBBAAABABBAABAAABAABABABAABAA​ABBABAABABABBBABAAABBAABBAABBBAABAAAABABABBBAABABBABABBABBBABABBAABAAAABBABAABBA​BAABAAABAAABBABBAABBAABAAABBABAAABAAABAA
↓
MAX ITLLPHKW BL GBGCHFXPMPH

Your job is to simply say the "secret word". No further hints will be given, it's already easy compared to some of the previous ones. Good luck.

is the code bacon?

セルティ・ストゥルルソン


GHAAAAAAAAAAAAAAAAAAAAAAAAAAH


Got it? :D More A's? :(((

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The answer's Code Geass. Whether you want it or not, Ninja! :<<<<