Question The Huskeh!!

[anoni]

Well you tried

So in a 1 x 1 grid, there would only be 1 square that was 1 x 1 large.

Therefore N₁ = 1; where N₁ is the amount of squares there are when N is equal to 1

In a 2 x 2 grid, there would only be 1 square that was 2 x 2 in the grid and there would be 4 squares (you can count them) that would be 1 x 1 in the grid

Therefore N₂ = 4 + 1 = 4 + N₁ (as N₁ was equal to 1)

Now N₂ = 4 + N₁, what does 4 and N₂ have in common? Well 4 is 2²! So what we have is

N₂ = 2² + N₁.


Now if we have 3 x 3 grid there would be 1 square of 3 x 3, 4 squares of 2 x 2 (you can count that) and 9 squares of 1 x 1 (you can also count that).

Therefore we have N₃ = 9 + 4 + 1, but we know that 1 is equal to N₁ and 4 = 2² so we get the this relationship

N₃ = 9 + 2² + N₁. Now we know that N₂ = 2² + N₁ So we can sub that in
N₃ = 9 + N₂

What do 9 and N₃  have in common? Well 9 = 3² so we get our final equation to be

N₃  = 3² + N₂



Do you see a pattern?

The pattern is this
N_k = k² + N_k-1   


Because of this we could expand this recursive relation

N_k = k² + (k - 1)² + (k - 2)² + .. + 2² + 1


So the final answer is this

The amount of squares for an N x N grid would be

1 + 4 + 9 + ... + (N - 1)²  + N²

I did it in a more rigorous way that was required, but do you understand?
 

[Lethrasherhuskeh]

I actually asked my sister about it, and she sorta broke it down for me after many drawings later. I'm pretty much like a primary schooler when it comes to maths so I needed her to draw it out as I understand diagrams better. I'm more of a visual kinda guy. But yeah, I do get the gist of it! ^^

Anymore questions?

[Luggz]

YES! I have another!

Have you ever sneezed so hard you have experienced recoil?

[Lethrasherhuskeh]

I think I did haha. But only when I was sick as shit. I think I get it from my dad: He would sneeze like he's trying to cough up some furball or something 

[Maine]

What would you do if you met a dragon IRL?

[Lethrasherhuskeh]

Woah dragons eh?

I think I'll prolly freak out first and shit my pants maybe xD If there was a wall or a structure or anything bigger than me except the dragon I'll run and hide, peaking out constantly to see what's up. Assuming that it won't gobble me up on sight, I'll just go up to it cautiously and maybe pet it after calming down many hours later xD

[Buna]

What would you do if you acquired the tardis. I'm just going to assume you know what that is...

[Luggz]

Shall we take over the world?

[Lethrasherhuskeh]

@Buna, okay I don't really watch a lot of Dr Who (only heard about it from friends and stuff), and I went to do a quick wiki search on what it is about. It's basically some device which can travel back and forth through time and space correct?


If I had it, I think I would try to solve all the mistakes I made in the past I guess. That, and oh, maybe try to also try to make the extra effort in wooing this girl I had a crush on in technical college. She's still single, but she thinks I'm not her type xD


@Luggz  WHY YES WE SHALL! 


TOGETHER WE ARE TEAM HUSKEH PINK FOX!

[Buna]

Have you ever eaten a battery.

[Lethrasherhuskeh]

Uh no...


I don't suppose you know of anyone who did...

[anoni]

What is your stance on current US politics

[Luggz]

What's your current stance?

[Buna]

If you got paid to dress up like a complete moron ,wear a crown, dance through walmart, and say "The king of dance has arrived'. Would you do it.

[Lethrasherhuskeh]

@anoni uhmm well its pretty neutral as I'm not really well verses with politics to begin with. But I tend to lean in a little when stuff happens if yknow what I mean.

@Luggz IM IN STEALTH STANCE!!

Lol just kidding. I don't really see how I have a stance at the current moment actually.

@Buna if I'm paid enough, then yes. xD

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