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-   -   A little thinking game.. (http://www.insidehoops.com/forum/showthread.php?t=272926)

 Richie2k6 07-29-2012 02:13 PM

A little thinking game..

I counted 40

 TheSilentKiller 07-29-2012 02:17 PM

Re: A little thinking game..

I only got 36, but I did it kind of fast.

EDIT: Just saw 4 more, making my total 40

 RaininTwos 07-29-2012 02:17 PM

Re: A little thinking game..

I'm stuck at 35

 Richie2k6 07-29-2012 02:20 PM

Re: A little thinking game..

not sure what the actual answer is.. I wonder if there's more than 40? :confusedshrug:

 DaHeezy 07-29-2012 02:22 PM

Re: A little thinking game..

34

Re: A little thinking game..

 Meticode 07-29-2012 02:35 PM

Re: A little thinking game..

40! Must look between the lines.

 Faptastrophe 07-29-2012 02:39 PM

Re: A little thinking game..

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.

Re: A little thinking game..

 dude77 07-29-2012 02:43 PM

Re: A little thinking game..

Quote:

nice :applause: .. I missed the last 'big ones'

 AK47DR91 07-29-2012 02:46 PM

Re: A little thinking game..

Oh, I missed the four 3x3 squares. No wonder I could only get 36.

 Faptastrophe 07-29-2012 03:10 PM

Re: A little thinking game..

Quote:
 Originally Posted by The Macho Man How are the L shaped tetris things squares? COME ON

What are you talking about? :oldlol:

 Myth 07-29-2012 06:41 PM

Re: A little thinking game..

I counted 40 when I saw this on Facebook.

 Myth 07-29-2012 06:44 PM

Re: A little thinking game..

Quote:
 Originally Posted by Faptastrophe What are you talking about? :oldlol:

Some people mistakenly count these due to getting in the habit of counting open spaces rather than squares:

 REACTION 07-29-2012 07:02 PM

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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