Challenge Math and Brain Teaser Problems!



a challenge my math teacher gave out was to prove the pythagorean theorem using a trapezoid,, i figured it out after like a week but not in class haha

i guess that works on this topic? prove the pythagorean theorem to be true with a trapezoid (using any formula regarding a trapezoid, or such)


Your welcome and thank you at the same time!
Yeah, I think homeschooling and the such can easily cause a lot of rants, I've done it myself (I feel like I'm missing out on things as well, like not going off to my full potential in this area) but here I go on a rant again!

I'm gonna look into the maze generator website in a bit (bio homework..). It looks really awesome and can't wait to check it out further! (I've actually wanted to do something of the like for a programming project or something).

I'm also really happy your enjoying my problems, math is fun to think about when you're bored in class (and ironically for me, in actual math class!). I have a friend who gives me math questions as well that are fun to do in spare time :slight_smile:


How about at the top 2 corners, you create a line down to the bottom. Then you have 2 right triangles surrounding a square or rectangle. That might be something..


If anything thanks for reviving, I'm more than glad to talk over old stuff!

It works for any triangle with that angle of 60° and not just equilateral triangles, and when I did it, I used the fact that it was the incenter of the triangle (along with some other things) ...ohhh I see what you mean! Using the incenter here the first time I'd learnt about it so I didn't (still don't) really know much.

:thinking: like i can't really think why it wouldn't work for all triangles now. (I wrote my answer for this ages ago and I just reposted the question for others... :upside_down:)


it's a good question! ^^ i can see why it was used to teach about the incenter.

i used this figure to prove it, but it can be done a variety of ways


I will be back later, (I have class hehe... :confused:) just quickly for @JonnyGamer:

  • thanks again and yes for me too it is in maths classes too that I look at these :joy: (along with all other classes...) I was just wondering if you set a reference length for your star-in-circle :smiley: (e.g. a side of unit length 1)

  • I have a more accessible thing for the maze graph, it is a drag and drop language called Edgy which I would love to go through :slight_smile:

Problem solving in general, algorithms, graph theory

Oh snap! I was so excited I forgot to give a reference unit! How about each graph square is a unit. I'll edit that in, thanks

Ooh! I can't wait to look into Edgy! (mazes are like my second favorite thing to do!)



Oh! You're talking about a right trapezoid. Sorry, I was mistaken. That looks like a pretty good proof to me, I think you'll be good


whoops #2: forgot to clarify all kinda of trapezoids were allowed

sorry for the confusion,, sfdfads

the star you drew on the graph paper looks really interesting, actually. in a sort of sophisticated-simplistic way.


Thanks! I guess it just goes to show how simple designs can be difficult to solve. I'm still wondering how to solve it. Probably using the distance forumula.


My initial instinct was "divide everything into triangles, triangles you can do things with", so I did, and my tired (11PM) brain somehow ran into the assumption that each of the "inner" spikes (ex. the one formed by angle E) was 6. But, upon closer inspection, of course—point E does not lie directly on a line.

I'm considering putting this problem into a different unit so that the points lie on lines, doing the calculations there, and then using scale factor to figure out how to turn the calculations in the different unit into the original one. Or maybe I'm just overthinking all this and need to sleep.


I don't know. I'm getting a very sleepy brain too (it's only 9!). I'll have to sleep on it and work tomorrow. It sounds as though that your getting somewhere and on the right track. In the meantime, I've got school work in need to finish.. ugh..


Good luck finishing that work, then. And good night! I'll try tackling this problem again in the morning ^^


Thanks! Sounds good. Bye


The question wasn't if a double negative is a positive.
So no, you didn't answer the problem.


:smiley: Haha funnily it wasn't actually about the incenter :thinking: but would be a nice way to illustrate!

And I was working on this, it was very fun hehe. (Couldn't use my iPad/Paper by FiftyThree so I was doing it on paper :stuck_out_tongue:) and I haven't transferred it over (although I love it, it takes too long hehe)

So here is my all-over-the-place working out:

Hmm so I got 33.941 sq units :thinking:

And I hadn't realised that you'd labelled them so oh dear I have different labels XD

More info on what I used:


No, that's not what I meant. You meant that -3 times -3 is nine, right? That's what I mean by a double negative is a positive.
I don't think that's the reason why it's that; but at least, I gotta add(?) something to the conversation...


Wow! Incredible work!
I know that the upper bound is 50 and the lower bound is 16. I'm gonna have a go at this during school, I'll see what I get! :slight_smile:


Ooh yes and we can check! :smile: and think about it together – I am not very sure about my answer!