Math Prob!

[z3ro]

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?

[gh0st]

I bet its 20x20

[theellimist]

800

[techb]

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.

[z3ro]

800

cOuld you explain please..?

[Kulverstukas]

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

[theellimist]

Exactly like this but larger:

[techb]

J

Exactly like this but larger:

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.

[Deque]

Exactly like this but larger:
 

 

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:



Which means you have 400 red squares in total (in every second line every second square is red: 40*40 / 4 = 400).
 

[theellimist]

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

Corners are not sides bro.

[techb]

Corners are not sides bro.

Corners where never mentioned in the problem.

[kateus]

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.

[theellimist]

Haha fuck me, I read the original problem wrong. In that case, I think Deque got it right.

[pl0tuS]

I think Deque is right. It follows the parameters.