NSFW Time for some Math

g💚jira · May 12, 2016, 04:16:34 PM

Let's divide a 1 x 1 square into rectangles. Each rectangle is colored blue or yellow. Additionally, the total blue area inside the square equal the total yellow area inside the square.

Now, the "number" of a rectangle varies on its color. In this problem, a blue rectangle's number is height/width, and a yellow rectangle's number is width/height.

So here's your task: Find the minimum value for the sum of all the rectangle numbers in the square.

i am karjala takaisin · May 12, 2016, 04:25:58 PM

easy shit my man

3b² + 7y + 2 = 0

-7±√7² - 4(3)(2)/2(3)

-7±√49 - 24/6

-7±√25/6

-7±5/6

-2/6 = -0.33333....

-12/6 = -2

Turkey · May 12, 2016, 04:40:06 PM

I'm confused by the second sentence; which colors are you using? Green/red or Blue/yellow?

g💚jira · May 12, 2016, 04:46:46 PM

OOPS

I had no blue/yellow pencils so I had to use green/red and got confused, sorry! Fixed, it should be blue/yellow.

Turkey · May 13, 2016, 07:36:45 PM

Sorry man, I honestly don't even understand what you're asking. I've been out of practice for a while and this abstract stuff was painful for me.

g💚jira · May 13, 2016, 07:54:17 PM

Quote from: HurtfulTurkey on May 13, 2016, 07:36:45 PM

Sorry man, I honestly don't even understand what you're asking. I've been out of practice for a while and this abstract stuff was painful for me.

No need to apologize. Honestly, I still don't know if my answer to the problem makes sense/is correct either.

I'll also update the OP with a [hopefully] clearer breakdown later when I get time.

Turkey · May 13, 2016, 07:57:30 PM

Quote from: 🎀 mathemaidician 🎀 on May 13, 2016, 07:54:17 PM

Quote from: HurtfulTurkey on May 13, 2016, 07:36:45 PM
Sorry man, I honestly don't even understand what you're asking. I've been out of practice for a while and this abstract stuff was painful for me.
No need to apologize. Honestly, I still don't know if my answer to the problem makes sense/is correct either.

I'll also update the OP with a [hopefully] clearer breakdown later when I get time.

I'm interested to see the explanation. It's kind of depressing to not even know how to start doing something like this anymore. Math is definitely a perishable skill.

maverick · May 13, 2016, 09:50:56 PM

I ended up with 5/2.

g💚jira · May 13, 2016, 11:51:07 PM

Quote from: James Lancaster on May 13, 2016, 09:50:56 PM

I ended up with 5/2.

Same! I'll post my sketchy proof when I get the time to organize it from a buncha schizophrenic notes [I basically used height-width ratios to prove yellow must add to 0.5, and blue must add to 2.0]. How'd you come about it?

maverick · May 14, 2016, 07:30:24 AM

Quote from: 🎀 mathemaidician 🎀 on May 13, 2016, 11:51:07 PM

Quote from: James Lancaster on May 13, 2016, 09:50:56 PM
I ended up with 5/2.
Same! I'll post my sketchy proof when I get the time to organize it from a buncha schizophrenic notes [I basically used height-width ratios to prove yellow must add to 0.5, and blue must add to 2.0]. How'd you come about it?

Same. I got that the numbers of one rectangle would have to be .5/1 and the other would have to be 1/.5 and added them together.

Desty · May 14, 2016, 08:09:05 AM

So how many rectangles are there? Or is this one of those problems where it doesn't matter the number 'cause the sum of both the colors' total can be achieved through deduction?

I'm not into math, but I kinda wanna know how to work this puzzle

2.5 is the easy answer since the areas both equal the same, thus one side must be 0.5 and the other 1, but surely there's more to it? If there isn't more to it, then this is literally grade school stuff. What am I missing?

g💚jira · May 14, 2016, 09:10:55 AM

Quote from: Desty on May 14, 2016, 08:09:05 AM

So how many rectangles are there? Or is this one of those problems where it doesn't matter the number 'cause the sum of both the colors' total can be achieved through deduction?

I'm not into math, but I kinda wanna know how to work this puzzle

2.5 is the easy answer since the areas both equal the same, thus one side must be 0.5 and the other 1, but surely there's more to it? If there isn't more to it, then this is literally grade school stuff. What am I missing?

I thin it's 2.5 too, but the hard part is making a general proof for the sides adding up to 2.5. The number of rectangles shouldn't matter. Or, if you can prove that there's only one arrangement, then it should [EDIT: Earlier I wrote that there are multiple arrangements of 2.5; I think there's a definitive way to prove that there's only one, my bad]

[I'll post my answer shortly, sorry for the delay]

Desty · May 14, 2016, 10:15:12 AM

Yeah, I can't find a value lower than 2.5

Unless you go into some reality warping math there really can't be a lower value, I think. You can go infintely bigger, but not smaller.

Area Value = Surface Area

Surface Area is 1/0.5 Therefore
Area Value can only be as low as 1/0.5

Desty · May 14, 2016, 10:18:01 AM

I accidentally clicked quote instead of edit without realizing it. Consider this a double post