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Old 07-29-2012, 08:02 PM   #16
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Default 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.
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Old 07-29-2012, 08:05 PM   #17
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Default 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.
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Old 07-29-2012, 08:09 PM   #18
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Default Re: A little thinking game..

I got 39 and I counted the big square.
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Old 07-29-2012, 08:10 PM   #19
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Default Re: A little thinking game..

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I just counted.

Well, what if it were a 100x100 square?
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Old 07-29-2012, 08:11 PM   #20
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Default Re: A little thinking game..

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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.
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Old 07-29-2012, 08:13 PM   #21
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Default 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]
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Old 07-29-2012, 09:58 PM   #22
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Default Re: A little thinking game..

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Originally Posted by b1imtf
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Old 07-29-2012, 10:00 PM   #23
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Default 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.
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Old 07-29-2012, 10:15 PM   #24
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Default Re: A little thinking game..

I counted 38 before I saw LEFT4DEAD's GIF.
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Old 07-29-2012, 10:50 PM   #25
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Default 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.
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Old 07-30-2012, 01:18 AM   #26
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Default Re: A little thinking game..

34 before I saw the gif.
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