Question

Question:

Answer 1

I believe in ye @paki , you can explain it :P

Answer 2

sorry man, no idea... confused...

Answer 3

SAME :) anyways thanks for the try.

Answer 4

@SolomonZelman please help here...

and pleasure....

Answer 5

To answer your question.

Why can't we guarantee that?

Answer 6

Well to be honest, I did not even understand the question.

Answer 7

when it say n*2 or n*3, and if n>1 does it mean 2*2=4 blocks or 6 blocks etc...

Answer 8

and is green and red in form of checkerboard or any arrangements?

Answer 9

Well, it says that all corners have to be of either color, so we can't guarantee anything.
I would guarantee that there is a square of such a size when n is 1.5 or less.

Answer 10

1.5 is not even discrete. o.O

Answer 11

and it says 4 corners, WT*

Answer 12

it is not an integer, but we can't have 1 square of 2 colors right? and then we certainly can't guarantee.

Answer 13

its say n>1 why is that?

Answer 14

lets say n*2 = 1*2 = 2 what does that mean?

Answer 15

@pgpilot326

Answer 16

I have an idea :D

Answer 17

\[\Large \left.\begin{matrix}\color{cyan}{\blacksquare}\color{cyan}{\blacksquare}\color{cyan}{\blacksquare} \\\color{cyan}{\blacksquare}\color{cyan}{\blacksquare}\color{cyan}{\blacksquare}\\\color{cyan}{\blacksquare}\color{cyan}{\blacksquare}\color{cyan}{\blacksquare}\\\color{cyan}{\blacksquare}\color{cyan}{\blacksquare}\color{cyan}{\blacksquare}\\\color{cyan}{\blacksquare}\color{cyan}{\blacksquare}\color{cyan}{\blacksquare}\\\color{cyan}{\blacksquare}\color{cyan}{\blacksquare}\color{cyan}{\blacksquare}\\\color{cyan}{\blacksquare}\color{cyan}{\blacksquare}\color{cyan}{\blacksquare} \end{matrix} \right.\]
Looks like a good place to start haha

NOW

Answer 18

Let's think columns :)
The first column, there are seven squares. At least four of them must be the same colour. Like... obviously haha ;)
[Verify that for yourself >:) ]

That majority colour... let's just assume it's green, coz you know, green is awesome :))

So, four these must be green..... randomly sprinkling green now...
\[\Large \left.\begin{matrix}\color{green}{\blacksquare}\color{cyan}{\blacksquare}\color{cyan}{\blacksquare} \\\color{green}{\blacksquare}\color{cyan}{\blacksquare}\color{cyan}{\blacksquare}\\\color{cyan}{\blacksquare}\color{cyan}{\blacksquare}\color{cyan}{\blacksquare}\\\color{cyan}{\blacksquare}\color{cyan}{\blacksquare}\color{cyan}{\blacksquare}\\\color{green}{\blacksquare}\color{cyan}{\blacksquare}\color{cyan}{\blacksquare}\\\color{cyan}{\blacksquare}\color{cyan}{\blacksquare}\color{cyan}{\blacksquare}\\\color{green}{\blacksquare}\color{cyan}{\blacksquare}\color{cyan}{\blacksquare} \end{matrix} \right.\]
I don't even care what the others are :D

Answer 19

Let's try to do our best NOT to form the rectangle as described :3
In the second column, there are four squares beside the ones in the first column marked green.

Crucially, THREE of those four squares have to be red, if you don't want to form that rectangle (prematurely, that is ;) )

So let's randomly sprinkle red. (It doesn't matter which of the seven in the first column are green, and it won't matter which three of the four in the second column corresponding to the four green in the first would be red)
\[\Large \left.\begin{matrix}\color{green}{\blacksquare}\color{cyan}{\blacksquare}\color{cyan}{\blacksquare} \\\color{green}{\blacksquare}\color{red}{\blacksquare}\color{cyan}{\blacksquare}\\\color{cyan}{\blacksquare}\color{cyan}{\blacksquare}\color{cyan}{\blacksquare}\\\color{cyan}{\blacksquare}\color{cyan}{\blacksquare}\color{cyan}{\blacksquare}\\\color{green}{\blacksquare}\color{red}{\blacksquare}\color{cyan}{\blacksquare}\\\color{cyan}{\blacksquare}\color{cyan}{\blacksquare}\color{cyan}{\blacksquare}\\\color{green}{\blacksquare}\color{red}{\blacksquare}\color{cyan}{\blacksquare} \end{matrix} \right.\]

Answer 20

Can you see it? Once we get to the third column, there are three squares beside the adjacent pairs of squares in green and red. THESE are those three squares.
\[\Large \left.\begin{matrix}\color{green}{\blacksquare}\color{cyan}{\blacksquare}\color{cyan}{\blacksquare} \\\color{green}{\blacksquare}\color{red}{\blacksquare}\color{black}{\blacksquare}\\\color{cyan}{\blacksquare}\color{cyan}{\blacksquare}\color{cyan}{\blacksquare}\\\color{cyan}{\blacksquare}\color{cyan}{\blacksquare}\color{cyan}{\blacksquare}\\\color{green}{\blacksquare}\color{red}{\blacksquare}\color{black}{\blacksquare}\\\color{cyan}{\blacksquare}\color{cyan}{\blacksquare}\color{cyan}{\blacksquare}\\\color{green}{\blacksquare}\color{red}{\blacksquare}\color{black}{\blacksquare} \end{matrix} \right.\]


Two of these have to be the same colour... and if you haven't already seen it, it doesn't matter which two of these share the same colour, or even WHAT colour they are... you WILL form that rectangle that we've so desperately been trying to avoid


What a waste of time!

HA HA HA

Just kidding :)

Answer 21

@PeterPan what you want to say. by making fun here...?

Answer 22

I'm having fun, not making fun ^_^
I think I gave a pretty neat answer :)

Answer 23

Lol peter :)

Answer 24

But in all seriousness, was I correct? :)

Answer 25

sorry no idea for this question... as you have explained in a broad way, so it may be correct

Answer 26

:(
Okay

Answer 27

@PeterPan ; You are going in a right direction but I did not get the last part.

Answer 28

Hint provided to me.

Answer 29

its all about possibilitis the thing is it doesnt mintion that how many squars should ne red or green , so i think its possible :P
here is someway that make it possible for n x 3

mm this is one way that make it
\(\Large \left.\begin{matrix}\color{green}{\blacksquare}\color{red}{\blacksquare}\color{green}{\blacksquare} \\\color{red}{\blacksquare}\color{green}{\blacksquare}\color{red}{\blacksquare}\\\color{green }{\blacksquare}\color{red}{\blacksquare}\color{green}{\blacksquare}\\\color{red}{\blacksquare}\color{green }{\blacksquare}\color{red}{\blacksquare}\\\color{green}{\blacksquare}\color{red}{\blacksquare}\color{green}{\blacksquare}\\\color{red}{\blacksquare}\color{green}{\blacksquare}\color{red}{\blacksquare}\\\color{green}{\blacksquare}\color{red}{\blacksquare}\color{green}{\blacksquare} \end{matrix} \right.\)

Answer 30

What I mean, @imer as soon as we get to the third column, the three squares marked black
\[\Large \left.\begin{matrix}\color{green}{\blacksquare}\color{cyan}{\blacksquare}\color{cyan}{\blacksquare} \\\color{green}{\blacksquare}\color{red}{\blacksquare}\color{black}{\blacksquare}\\\color{cyan}{\blacksquare}\color{cyan}{\blacksquare}\color{cyan}{\blacksquare}\\\color{cyan}{\blacksquare}\color{cyan}{\blacksquare}\color{cyan}{\blacksquare}\\\color{green}{\blacksquare}\color{red}{\blacksquare}\color{black}{\blacksquare}\\\color{cyan}{\blacksquare}\color{cyan}{\blacksquare}\color{cyan}{\blacksquare}\\\color{green}{\blacksquare}\color{red}{\blacksquare}\color{black}{\blacksquare} \end{matrix} \right.\]
No matter how you colour these three in red or green, you will inevitably form a rectangle with four corners of the same colour... that's because two of the three will have to be the same colour.

Answer 31

Wait so what does n*2 and n*3 means, does 2&3 number of squares?

Answer 32

@ikram002p : can you please elaborate the question?