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07-29-2012, 08:02 PM   #16
REACTION
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Re: A little thinking game..

Quote:
 Originally Posted by Faptastrophe An n x n grid will have a total of n2 + (n - 1)2 + ... + 22 + 12 squares. The picture has one 4 x 4 square and two 2 x 2 squares. There are 42 + 32 + 22 + 12 = 16 + 9 + 4 + 1 = 30 squares in the 4 x 4, and there are 22 + 12 = 4 + 1 = 5 squares in each 2 x 2. Thus, there are a total of 30 + 2 * 5 = 40 squares.

Do you mean n^2 instead of n2? Not sure what formula you're using. But I'm assuming those are meant to be powers instead of multipliers, right?

The formula for the larger squares that makes sense to me is f(x) = (x(x+1)(2x+1))/6 where x = 4. f(4) gives you (4 * 5 * 9)/6 = 30 total squares for the larger ones. Then I'd add the 10 total combinations of the smaller squares. I think we're basically doing the same thing to arrive at 40 though.

07-29-2012, 08:05 PM   #17
Myth
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Re: A little thinking game..

Quote:
 Originally Posted by REACTION Do you mean n^2 instead of n2? Not sure what formula you're using. But I'm assuming those are meant to be powers instead of multipliers, right? The formula for the larger squares that makes sense to me is f(x) = (x(x+1)(2x+1))/6 where x = 4. f(4) gives you (4 * 5 * 9)/6 = 30 total squares for the larger ones. Then I'd add the 10 total combinations of the smaller squares. I think we're basically doing the same thing to arrive at 40 though.

I just counted.

 07-29-2012, 08:09 PM #18 ballup Your Favorite Canadian     Join Date: Dec 2010 Location: Boston's Tremendous Estate Posts: 6,378 Re: A little thinking game.. I got 39 and I counted the big square.
07-29-2012, 08:10 PM   #19
REACTION
HYRYST?

Join Date: Dec 2011
Posts: 661
Re: A little thinking game..

Quote:
 Originally Posted by Myth I just counted.

Well, what if it were a 100x100 square?

07-29-2012, 08:11 PM   #20
Myth
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Location: Orange County
Posts: 20,267
Re: A little thinking game..

Quote:
 Originally Posted by REACTION Well, what if it were a 100x100 square?

Then a math formula would be more necessary, but for this it is just overkill because I counted them in less than 10 seconds.

07-29-2012, 08:13 PM   #21
b1imtf
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Join Date: Feb 2011
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Posts: 4,765
Re: A little thinking game..

Quote:
 Originally Posted by Faptastrophe An n x n grid will have a total of n2 + (n - 1)2 + ... + 22 + 12 squares. The picture has one 4 x 4 square and two 2 x 2 squares. There are 42 + 32 + 22 + 12 = 16 + 9 + 4 + 1 = 30 squares in the 4 x 4, and there are 22 + 12 = 4 + 1 = 5 squares in each 2 x 2. Thus, there are a total of 30 + 2 * 5 = 40 squares.
[IMG][/IMG]

07-29-2012, 09:58 PM   #22
Richie2k6
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Re: A little thinking game..

Quote:
 Originally Posted by b1imtf [IMG][/IMG]

07-29-2012, 10:00 PM   #23
Faptastrophe
Rivalries Never Die

Join Date: Dec 2011
Location: LV
Posts: 3,568
Re: A little thinking game..

Quote:
 Originally Posted by REACTION Do you mean n^2 instead of n2? Not sure what formula you're using. But I'm assuming those are meant to be powers instead of multipliers, right? The formula for the larger squares that makes sense to me is f(x) = (x(x+1)(2x+1))/6 where x = 4. f(4) gives you (4 * 5 * 9)/6 = 30 total squares for the larger ones. Then I'd add the 10 total combinations of the smaller squares. I think we're basically doing the same thing to arrive at 40 though.

 07-29-2012, 10:15 PM #24 Scholar Nashty & Gawdbe FTW     Join Date: Dec 2010 Location: 16 Banners Deep Posts: 8,900 Re: A little thinking game.. I counted 38 before I saw LEFT4DEAD's GIF.
 07-29-2012, 10:50 PM #25 Eat Like A Bosh Banned     Join Date: Jan 2011 Location: Inside LeBron's head Posts: 5,180 Re: A little thinking game.. 36. EDIT: never mind saw Left4Dead's Gif Last edited by Eat Like A Bosh : 07-29-2012 at 10:54 PM.
 07-30-2012, 01:18 AM #26 JustinJDW ....     Join Date: Sep 2008 Location: Los Angeles, CA Posts: 4,501 Re: A little thinking game.. 34 before I saw the gif.

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