Math Contest #16 [1 SBI]

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Here you can keep your brain fit by solving math related problems and also earn SBI or sometimes other rewards by doing so.
The problems usually contain a mathematical equation that in my opinion is fun to solve or has an interesting solution.
I will also only choose problems that can be solved without additional tools(at least not if you can calculate basic stuff in your head), so don't grab your calculator, you won't need it.
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Every friday and tuesday!

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Rules

No upvote, No resteem, No follow required!

I will give 1 SBI to 1 random person who put a correct solution of the problem in a comment.

You have 48 hours to solve it.

Some additional rules for the case that the problem is an equation or a collection of equations.

In case there are multiple solutions, you have a higher chance of winning if you get all of them correctly.

Solutions can sometimes also be general like x = 20, y > -1. If there are multiple solutions submitted, that are part of the same general solution, they will be counted as one solution.

And one more thing: If there are infinitely many solutions, I only want integer solutions!

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Problem

Today I want you to draw me a tesseract(on a piece of paper or in the painting program of your choice).
If you know what that is: Go ahead, draw it!
If not, here a small explanation:
Similar to how a 2D square is the connection of two 1D lines
and similar to how a 3D cube is the connection of two 2D squares,
the 4D tesseract is the connection of two 3D cubes:
tes.png
It's basically the 4D equivalent of a cube or square.
Due to this fact the tesseract or any higher dimensional equivalent are also called "hypercube".
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To everyone who already participated in a past contest, come back today and try a new problem(tell me if you don't want to be tagged):
@addax @ajayyy @athunderstruck @bwar @contrabourdon @golddeck @heraclio @hokkaido @iampolite @masoom @mmunited @mytechtrail @onecent @sidekickmatt @sparkesy43 @syalla @tonimontana @vote-transfer @zuerich

In case no one gets a result(which I doubt), I will give away the prize to anyone who comments.

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@contrabourdon sponsors this contest with 2 STEEM weekly.
You can support him by using a witness vote on untersatz, so he can further support this and other contests.



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7 comments
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To listen to the audio version of this article click on the play image.

Brought to you by @tts. If you find it useful please consider upvoting this reply.

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w3389un2o1.jpg
My attempt at what I think you want.

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(Edited)

Can you maybe change the relative position of the cubes, so I can easier differentiate all the lines?

By the way: changing the relative position of the cubes changes rotation of the tesseract in 4d.

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(Edited)

Well, that was fun!
It took an hour to finish.
One time I started over completely.
Sorry about the erased lines!
As long as you don't ask me to solve
to figure the volume, I'll be happy!
@quantumdeveloper
7s4xerntb8.jpg

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Looks good.
By the way 4d-volume wouldn't be too hard to calculate:
The 2D-volume of a square is V₂ = A = a².
The 3D-volume of a cube is V₃ = a³.
→The 4D-volume of a tesseract is V₄ = a⁴.

Although its so counterintuitive to make sense of these higher dimensions, the math of it is mostly as easy as for the lower dimensional counterpart.

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