How Many Triangles?

ren wrote:

Malcolm Serenity wrote:

ren wrote: that's what i call dimensions. I looked at it in a sort of distorted 3d space. Like a non-cubic 4x4x4 cube of sorts

Ahh. That makes sense!

really? When I do stuff like this it makes me feel like I'm about to discover the solution to ftl or time travel

how did you go about it?

Hahaha. I did it based off a a simple equation. For any "How many triangles" that are set up in this same way (intersecting lines originating from 2 vertices), you take the number of unique lines that originate from one of the bottom vertices and cube it. Thus, if you count the unique lines in the left or right vertices, you get 4. Cube it, and you get 64.

If you take just a plain triangle, there is only one unique line from each of the vertices. Thus, you get 1 triangle.


If you add a new line to each vertex, you will find that you can form 8.


Thus, 3 unique is 27.


And finally, 4 unique is 64

I know the math, but I was having a herd time visualizing all the variables. (probably spent too much time at work)

So I wrote down all the ones I could find. Or, I made a picture.

Wescli Wardest wrote: I know the math, but I was having a herd time visualizing all the variables. (probably spent too much time at work)

So I wrote down all the ones I could find. Or, I made a picture.

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Another excellent way of solving

I have an answer for you, but you're not going to like it. Technically, if you went down into the very smallest particle break down of triangles the answer would continue on forever until it reached a point that it could go no further. Therefore, to simplify it the answer it translates into:

∞

Or better yet:

4. Challenge me, I'll prove it. LMAO!

There is only 1 triangle, at any one time else the shape would not be a triangle. :dry:

Being silly of course... as the question is how many triangles occur in the prescribed pattern and I got to about 23 or 24 and then saw the other posts here with the answer. Oh thank you for saving me time
:silly:

Answer 64.


Sites with the answer.
Website:
http://scienceblogs.com/startswithabang/2012/07/28/weekend-diversion-triangles-a-puzzle-and-beauty/

Here is a youtube video of the count. It shows all the counting from left and right side then eliminates double counts.
http://www.youtube.com/watch?v=MUrkkoKbzWE Answer 64.