# The Rug Puzzle: how many triangles?

A quick maths puzzle I need your help with:
so earlier this week a viewer, Andres,
emailed me a photo of the new rug they had just got.
And when they got it home, their eight-year-old child looked at it and said,
"Well how many triangles are there?"
Andres is like, "Well, you know, we can count them!"
And the small ones are pretty straightforward.
The rug is 18 rows high. It's 20 columns across.
There are two little triangles per rectangle. That's a total of 720 little triangles.
"and this one and that one and that one and that-"
I mean there's loads of... okay enough!
There are loads of possible triangles in that rug.
So Andres emailed me to say, 'Is there an interesting way to do this?'
I'm like, 'I'm not sure I'll give it a go!'
But then I thought, let's open it up to the Internet.
So yesterday, I tweeted this as a challenge and loads of people got involved.
Some people did working out by hand, some people wrote computer code.
Andres also chipped in with a link to where the original rug came from so you can get a nice clean shot of it.
And someone did an animation trying to show how many triangles there are which- okay enough!
Which, as well as doing my head in,
That is the animation I used earlier on. I mapped that onto the original photograph
just to illustrate how many triangle possibilities there are.
So this is it! Everyone, we need to have a go at this puzzle.
You don't have to start with the whole rug. I mean, just that- come on!
You can count that many triangles!
I'll put a link to that file underneath, print it out.
Count the triangles. See if you can scale all that up.
If you get an answer at the end, chuck it in the comments, tweet it, email it to me.
If we get a sufficiently interesting valid answer. I will do a follow-on video
and actually Andres and I both haven't had time to try it ourselves
I'll do a follow-on video
but at the very least I mean there is an eight-year-old child out there
counting on us to count those triangles, so everyone get involved.
I believe in you, off you go!
And while we're here, a quick hello to all the people who watch right to the very end - the hardcore fans!
You're my people! So thanks watching the video, as always.
I thought I'd just mention this you know the face thing that's going on.
I'm not growing a beard. This is not permanent.
I simply haven't left the house much in the last two-and-a-half weeks
I've been outside twice because the second draft, (which is pretty much the final draft) of my new book is due.
So I've been doing nothing but that for a while now.
Publishing takes forever, by the way, so it won't be out until the 2nd of Novermber.
So I'm going to get back to writing it now, it'll be out before Christmas.
Once I finish writing the draft, then I'll try the rug puzzle.
Of course my previous book, 'Things to Make and Do in the 4th Dimension', that is available - all the usual places.
Although if you buy it from Maths Gear it'll be signed by me. I sign all the copies on Maths Gear.
So if you can be bothered getting a signed copy, you're also supporting my website trying to promote a wide range of ridiculous math toys,
so there you are: Maths Gear! For all your math toy needs.
I've just decided this video is officially sponsored by Maths Gear!
I've just sponsored my own video.