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Encyclopedia Galactica => Science => : z3ro July 28, 2012, 11:10:44 AM

: Math Prob!
: z3ro 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?

: Re: Math Prob!
: gh0st July 28, 2012, 06:41:29 PM

I bet its 20x20

: Re: Math Prob!
: theellimist July 28, 2012, 09:21:51 PM

800

: Re: Math Prob!
: techb 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.

: Re: Math Prob!
: z3ro July 29, 2012, 04:07:46 AM

: theellimist  July 28, 2012, 09:21:51 PM

800

cOuld you explain please..?

: Re: Math Prob!
: Kulverstukas July 29, 2012, 08:25:35 AM

My calculations are showing that this might be just a little over nine thousand.

: Re: Math Prob!
: theellimist July 29, 2012, 09:18:10 AM

Exactly like this but larger:

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

: Re: Math Prob!
: techb July 29, 2012, 09:50:16 AM

J

: theellimist  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.

: Re: Math Prob!
: Deque July 29, 2012, 09:58:25 AM

: theellimist  July 29, 2012, 09:18:10 AM

Exactly like this but larger:
 

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

 

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).
 

: Re: Math Prob!
: theellimist July 30, 2012, 12:25:40 AM

: Deque  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.

: Re: Math Prob!
: techb July 30, 2012, 12:41:38 AM

: theellimist  July 30, 2012, 12:25:40 AM

Corners are not sides bro.

Corners where never mentioned in the problem.

: Re: Math Prob!
: kateus July 30, 2012, 02:48:22 AM

: theellimist  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.

: Re: Math Prob!
: theellimist 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.

: Re: Math Prob!
: pl0tuS July 30, 2012, 05:49:26 AM

I think Deque is right. It follows the parameters.