# Challenge Math and Brain Teaser Problems!

Spoiler! Don't open if you're figuring it out still!

It's 87!

Also, do any of you have the game Tricky? It's a brain-teaser/logic game. It's frustrating but fun, I recommend it!

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Oooh yay let's do this together!!

It looks like there are a lot of parts to it

Must go, I will be back later

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A Hopscotch variable only has a max of 7 digits.
I plan to make my project handle up to 20 digit variables.

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Okay this is a start diagram (I have more working out in my books but not on iPad yet)

And then I used sine rule the orange length and the length in red in terms of x (I know it is just one unit length but I set it to x anyway for generalisation ) and that is where I am up to, hopefully I can show that on Paper later

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Now here are the orange and red lengths

Edit: whoops I did a mistake, I need to fix that up. Wait it seemed to be okay actually. Let me know if Iâve made any mistakes.

More on the things that I used hereâ

Symmetry for sin(180Â° - Î¸) = sin(Î¸):

Double angle identities/formulae - expansion of sin(2Î¸):

Now we can find the area of one of the orange triangles, there is a way of finding the area of a triangle using two sides and an angle between them:

As for the circle and the inscribed regular pentagon, at the moment I have an idea for using area of segments in circles

https://www.mathsisfun.com/geometry/circle-sector-segment.html

Edit: hmm I donât actually know if there are other unshaded parts in the circle that arenât clear at firstâŚ

And whoops this wasnât meant to be just me going off on a tangent, this was just what I was exploring

This has freed me from a lot of boredom, thanks so much @JonnyGamer

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https://www.tynker.com/play?p=590c05a91c36d1f40a8b456e#/

Here is a quick "Collatz" machine made with Tynker.'
It's pretty easy to use.
It worked with 20 digit numbers.
I don't know what's the max digit sized numbers that the project can use.
I slowed the projects speed down a little, so the user can see the variable as it changes.
Without the slowdown, it takes less than 2 seconds to get to 1 using a 20 digit variable

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Cool. I am making a similar program using Swift.

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Ooh that is very cool

I implemented the pseudocode that I put before, in Hopscotch:

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I have a quick one for everyone

What is the only number that, when spelled in English, that has all its letters in alphabetical order?

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Is it forty.
I'll check out your Hopscotch project.
I used the same type of code you showed a pic of.

@MR.GAM3R
That's great.
When you have finished making+using your Swift version, can you tell me what's the max digit number you can use before letters like "e" are used in the number value?
The Tynker version i made started using letters when a variable had 23 digits.
I haven't started the Construct version yet.

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Yes it is hehe

There is another one (not about alphabetical order but still wordplay):

Which is the only number, in the English language, which has the same number of letters in its name as its numerical value?

And the code in the Hopscotch project is just the same as the pseudocode that I put earlier so it is not really anything although I should have checked more closely if it was working correctly...

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four!!!

Oh no it's wrong.

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...

Haha I was about to say that I was reflecting on the mathematical side of it too, then realised I was making some assumptions.

Is there a case where it will not work?

Oh wait, I thought you meant the Collatz Conjecture But was it for the number?

Four was the answer from what I had read although I didn't think to question it thoroughly for other numbers...

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Hehe q r s t u
R is before u

But that was really close (I don't the answer but you were close as in it could of been it)

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I got confused. i was thinking alphabetical order of the letters

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@t1_hopscotch do you know any other brain teasers??

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Ohhh I see whoops I will edit to clarify that the alphabetical order isnât related here haha, it was just related in looking at the names of the words. I have Murderous Maths to thank for those:

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Oh, you meant that oops @t1_hopscotch , sorry @Stradyvarious, what I said wasn't necessary,
(I thought you meant like abc as in what's the only number that's in alphabetical order)

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Whats the square root of nine?

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3 that's easy XD

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