/sci/ - Science & Math » Thread #13950569

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Anonymous Sat 11 Dec 14:45:16 2021 No.13950569 View Reply Original Report

Quoted By: >>13950579 >>13950588

You are given 11 squares with side length 1. What's the smallest side length of a square that can fit all 11 squares without them overlapping?

Anonymous

Anonymous Sat 11 Dec 2021 14:47:28 No.13950579 Report

Quoted By:

>>13950569
Pretty sure you can just bruteforce this one in 2 minutes...

Anonymous

Anonymous Sat 11 Dec 2021 14:48:46 No.13950588 Report

Quoted By: >>13950590

>>13950569
3*3 is too small. 4*4=16.

Anonymous

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Anonymous Sat 11 Dec 2021 14:50:07 No.13950590 Report

Quoted By: >>13950596 >>13950642

>>13950588
the question is obviously to find an arrangement that's better than 4*4

Anonymous

Anonymous Sat 11 Dec 2021 14:51:23 No.13950596 Report

Quoted By: >>13950597

>>13950590
It does say "square", doesn't it?

Anonymous

Anonymous Sat 11 Dec 2021 14:52:02 No.13950597 Report

Quoted By: >>13950608

>>13950596
yes

Anonymous

Anonymous Sat 11 Dec 2021 14:54:41 No.13950608 Report

Quoted By: >>13950610

>>13950597
Then you can't do better than 4*4. Non-integer side-lengths can only be attained if you waste space for no gain.

Anonymous

Anonymous Sat 11 Dec 2021 14:55:44 No.13950610 Report

Quoted By: >>13950616

>>13950608
try harder

Anonymous

Anonymous Sat 11 Dec 2021 14:56:30 No.13950616 Report

Quoted By: >>13950627

>>13950610
Cope. You can't do better than 4*4. If you don't understand this, try it with 2 or 3 squares.

Anonymous

Anonymous Sat 11 Dec 2021 15:00:55 No.13950627 Report

Quoted By:

>>13950616
we're not talking about 2 or 3, we're talking about 11.

Anonymous

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Anonymous Sat 11 Dec 2021 15:03:56 No.13950642 Report

Quoted By: >>13950647

>>13950590
3*3 is too small
4*4 is the smallest integer side square
does there exist a 3.?? sided square that can fit more than 9 unit squares?
no, since to fit another more than 9 squares you necessarily need at least one row/column of 4 squares
so a square with side a doesn't fit more squares a square with side floor(a)
so 4*4 is the minimum

picrel is an example of square with side about 3.5

Anonymous

Anonymous Sat 11 Dec 2021 15:05:02 No.13950647 Report

Quoted By: >>13950680 >>13951262 >>13951493

>>13950642
you are allowed to rotate the squares

Anonymous

Anonymous Sat 11 Dec 2021 15:11:13 No.13950680 Report

Quoted By: >>13950692

>>13950647
>you are allowed to rotate the squares
Maybe you should have stated that in your OP, you little gaslighting shit.

Anonymous

Anonymous Sat 11 Dec 2021 15:13:55 No.13950692 Report

Quoted By: >>13950751

>>13950680
why would you ever assume you can't? read the op carefully

Anonymous

Anonymous Sat 11 Dec 2021 15:26:36 No.13950751 Report

Quoted By: >>13951027

>>13950692
>why would you ever assume you can't?
Seems to be the intuitive interpretation for most people.

Anonymous

Anonymous Sat 11 Dec 2021 16:47:29 No.13951027 Report

Quoted By:

>>13950751
packing theory, it's a thing.

Anonymous

Anonymous Sat 11 Dec 2021 16:55:34 No.13951048 Report

Quoted By: >>13951061 >>13951245

It's very easy to show that if a better square than 4*4 exists, it must have side-length exactly sqrt(11). From there I'm not sure. I will work on it a bit.

Anonymous

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Anonymous Sat 11 Dec 2021 17:02:04 No.13951061 Report

Quoted By:

>>13951048
>It's very easy to show that if a better square than 4*4 exists, it must have side-length exactly sqrt(11)
It's very easy to see that can't possibly be the case, becuase that would imply a perfectly tight fit, and it's very easy to see that's impossible.

Anonymous

Anonymous Sat 11 Dec 2021 18:09:15 No.13951245 Report

Quoted By:

>>13951048
Hint: there are multiple better squares, none of them are as good sqrt(11)

Anonymous

Anonymous Sat 11 Dec 2021 18:13:46 No.13951262 Report

Quoted By: >>13951499

>>13950647
Well then they're diamonds.

Anonymous

Anonymous Sat 11 Dec 2021 19:08:51 No.13951485 Report

Quoted By:

It's not possible less than of 4x4 because the squares are a discrete area, and can only be positioned with all of its points relative to eachother and cannot be cut.

Anonymous

Anonymous Sat 11 Dec 2021 19:12:07 No.13951493 Report

Quoted By:

>>13950647
Either a retard or completely disingenous Regardless OPs a faggot

Anonymous

Anonymous Sat 11 Dec 2021 19:14:51 No.13951499 Report

Quoted By:

>>13951262
Yep. That's how I became a billionare. I started rotating all of my squares into diamons.

Anonymous

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Anonymous Sat 11 Dec 2021 19:24:50 No.13951536 Report

Quoted By: >>13952388

Packing problems are funny.

Anonymous

Anonymous Sat 11 Dec 2021 22:42:38 No.13952130 Report

Quoted By: >>13952162 >>13952188

why would people read a question meant to challenge them and then assume the one unstated property that makes the question completely uninteresting

Anonymous

Anonymous Sat 11 Dec 2021 22:54:16 No.13952162 Report

Quoted By: >>13952188

>>13952130

This.
If you can't rotate them it is a question for brainlets..

Anonymous

Anonymous Sat 11 Dec 2021 23:02:24 No.13952188 Report

Quoted By:

>>13952130
>>13952162
We haven't had a Monty Hall thread in a while. Where are you two from, newfriends?

Anonymous

Anonymous Sun 12 Dec 2021 00:15:23 No.13952388 Report

Quoted By: >>13952417

>>13951536
no they're not unless we're talking close packing of equal spheres.
you provide a solution to a problem that doesn't exist. you make a different box and pack less or more than 11 in it

Anonymous

Anonymous Sun 12 Dec 2021 00:24:23 No.13952416 Report

Quoted By:

The smallest side length of a square that can fit all 11 squares without them overlapping is the fucking coffin I bury the moron manager in that screwed up so I have to ship 11 fucking boxes instead of the 4 or 27 that fit perfectly inside a cube that is 30% cheaper than a fucking flatpack.

Anonymous

Anonymous Sun 12 Dec 2021 00:25:01 No.13952417 Report

Quoted By:

>>13952388
>unless we're talking close packing of equal spheres.
Squares are spheres if you use Linfinity

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