EvilZone

Encyclopedia Galactica => Science => Topic started by: z3ro on July 28, 2012, 11:10:44 AM

Title: Math Prob!
Post by: z3ro on July 28, 2012, 11:10:44 AM
A 40x40 white squareis divided into 1x1 squares by lines parallel to its sides. Some of these 1x1 squares are coloured red so that each of the 1x1 squares, regardless of whether it is coloured red or not, shares a side with at most one red square (not counting itself).
What is the largest possible number of red squares?
Title: Re: Math Prob!
Post by: gh0st on July 28, 2012, 06:41:29 PM
I bet its 20x20
Title: Re: Math Prob!
Post by: theellimist on July 28, 2012, 09:21:51 PM
800
Title: Re: Math Prob!
Post by: techb on July 28, 2012, 10:25:31 PM
I'm horrid at word problems, especially if it deals with geometry.

Is there an image accompaning the problem?

@limitless, how did you come up with the answer? Better to teach how to fish than to give it away.
Title: Re: Math Prob!
Post by: z3ro on July 29, 2012, 04:07:46 AM
Quote from: theellimist on July 28, 2012, 09:21:51 PM
800


cOuld you explain please..?
Title: Re: Math Prob!
Post by: Kulverstukas on July 29, 2012, 08:25:35 AM
My calculations are showing that this might be just a little over nine thousand.
Title: Re: Math Prob!
Post by: theellimist on July 29, 2012, 09:18:10 AM
Exactly like this but larger:

(http://images.kaneva.com/filestore4/3492062/4087484/checkerboard.gif)
Title: Re: Math Prob!
Post by: techb on July 29, 2012, 09:50:16 AM
J
Quote from: theellimist on July 29, 2012, 09:18:10 AM
Exactly like this but larger:

(http://images.kaneva.com/filestore4/3492062/4087484/checkerboard.gif)

Then the solution is mtiply the NxN then devide by two since it is either white or red. My thoughts only though. I am by no means a math guy.
Title: Re: Math Prob!
Post by: Deque on July 29, 2012, 09:58:25 AM
Quote from: theellimist on July 29, 2012, 09:18:10 AM
Exactly like this but larger:
 
(http://images.kaneva.com/filestore4/3492062/4087484/checkerboard.gif)

 

Quote
each of the 1x1 squares [...] shares a side with at most one red square

Your white squares share sides with four red squares, which is too much.

I believe the maximum is a pattern like this one:

(http://s1.directupload.net/images/120729/tst3d9n8.png)

Which means you have 400 red squares in total (in every second line every second square is red: 40*40 / 4 = 400).
 
Title: Re: Math Prob!
Post by: theellimist on July 30, 2012, 12:25:40 AM
Quote from: Deque on July 29, 2012, 09:58:25 AM
Your white squares share sides with four red squares, which is too much.
Corners are not sides bro.
Title: Re: Math Prob!
Post by: techb on July 30, 2012, 12:41:38 AM
Quote from: theellimist on July 30, 2012, 12:25:40 AM
Corners are not sides bro.

Corners where never mentioned in the problem.
Title: Re: Math Prob!
Post by: kateus on July 30, 2012, 02:48:22 AM
Quote from: theellimist on July 30, 2012, 12:25:40 AM
Corners are not sides bro.


Yeah, but assuming that your black squares are red squares, most of the white square in that picture would share edges with up to 4 red(black) squares which go against the parameters of the problem.
Title: Re: Math Prob!
Post by: theellimist on July 30, 2012, 05:41:21 AM
Haha fuck me, I read the original problem wrong. In that case, I think Deque got it right.
Title: Re: Math Prob!
Post by: pl0tuS on July 30, 2012, 05:49:26 AM
I think Deque is right. It follows the parameters.