Squares
Feb 10, 2013 10:03:12 #
How many can you create from this, assume square even if not perfectly square.
Feb 10, 2013 11:27:41 #
Feb 10, 2013 11:46:59 #
There are 38. Being a math nerd, I figured out the pattern to ones like this:
There is 1 large square
There are 16 small, 1x1 squares
There are 9 2x2 squares
There are 4 3x3 squares
There are 8 of the tiny interior squares
The pattern for a problem like this, not including the tiny added squares:
Take any n x n box, say a 5 x 5 box. The number of total squares can be found by adding: (5 x 5) + (4 x 4) + (3 x 3) + (2 x 2) + 1.
An 8 x 8 picture would have 64 + 49 + 36 + 25 + 16 + 4 + 1 squares, which would be 196 total squares.
Class dismissed.
There is 1 large square
There are 16 small, 1x1 squares
There are 9 2x2 squares
There are 4 3x3 squares
There are 8 of the tiny interior squares
The pattern for a problem like this, not including the tiny added squares:
Take any n x n box, say a 5 x 5 box. The number of total squares can be found by adding: (5 x 5) + (4 x 4) + (3 x 3) + (2 x 2) + 1.
An 8 x 8 picture would have 64 + 49 + 36 + 25 + 16 + 4 + 1 squares, which would be 196 total squares.
Class dismissed.
Feb 10, 2013 11:55:24 #
Bruce M. wrote:
How many can you create from this, assume square even if not perfectly square.
I got 36 and assume there are likely more, "not perfectly square" creates a ringer. Mine are all perfect squares assuming the original is all perfect squares
Feb 10, 2013 12:22:09 #
Math Nerd
there are 38. Being a math nerd, I figured out the pattern to ones like this:
There is 1 large square
There are 16 small, 1x1 squares
There are 9 2x2 squares
There are 4 3x3 squares
There are 8 of the tiny interior squares
Ok but start your 3x3 squares from each corner the number goes up quite a bit.
there are 38. Being a math nerd, I figured out the pattern to ones like this:
There is 1 large square
There are 16 small, 1x1 squares
There are 9 2x2 squares
There are 4 3x3 squares
There are 8 of the tiny interior squares
Ok but start your 3x3 squares from each corner the number goes up quite a bit.
Feb 10, 2013 12:28:02 #
Bruce M. wrote:
Math Nerd
there are 38. Being a math nerd, I figured out the pattern to ones like this:
There is 1 large square
There are 16 small, 1x1 squares
There are 9 2x2 squares
There are 4 3x3 squares
There are 8 of the tiny interior squares
Ok but start your 3x3 squares from each corner the number goes up quite a bit.
there are 38. Being a math nerd, I figured out the pattern to ones like this:
There is 1 large square
There are 16 small, 1x1 squares
There are 9 2x2 squares
There are 4 3x3 squares
There are 8 of the tiny interior squares
Ok but start your 3x3 squares from each corner the number goes up quite a bit.
I don't know what you're referring to. There are only four 3x3 squares. Use a different color pencil to outline them and you'll see that my answer is correct for the main drawing.
And I just now realized the answer to the problem is 40, not 38, because I failed to recognize that there are 10, not eight, of the tiny added squares in the interior.
Feb 10, 2013 12:55:07 #
Feb 10, 2013 13:11:06 #
Bruce M. wrote:
tchmath keep looking.... Step out of the box, so to speak.
Sorry, you're just wrong. As long as all of the boxes are assumed to be squares to begin with, the answer is 40. Number the boxes, highlight them with colors, anyway you want. The number is 40. No more, no less.
Feb 10, 2013 13:28:35 #
So Tschmath, is it 40?, or 196, or 196 +8 or... 196 + 10.. or 196 + 18... or .....
I am liking the number 40 but I am wondering what happened to 196 + 10....
I don't see how starting the 3 square boxes from the corners changes anything, any 3x3 box already extends to the one of the corners.
I am liking the number 40 but I am wondering what happened to 196 + 10....
I don't see how starting the 3 square boxes from the corners changes anything, any 3x3 box already extends to the one of the corners.
Feb 10, 2013 13:52:39 #
Feb 10, 2013 13:53:12 #
Blurryeyed wrote:
So Tschmath, is it 40?, or 196, or 196 +8 or... 196 + 10.. or 196 + 18... or .....
I am liking the number 40 but I am wondering what happened to 196 + 10....
I don't see how starting the 3 square boxes from the corners changes anything, any 3x3 box already extends to the one of the corners.
I am liking the number 40 but I am wondering what happened to 196 + 10....
I don't see how starting the 3 square boxes from the corners changes anything, any 3x3 box already extends to the one of the corners.
The 196 number was just an illustration of how the problem worked for any size square. The one in the OP was a 4x4 square, and I was showing how it would work for an 8x8 square, thus the 196. The answer to the OP's question is 40.
In the 4x4 square, there is only 1 4x4 square. If you start from the upper left corner, there is also a 3x3 square. Move the starting point from the upper left corner 1 space to the right, and you have another 3x3 square. Move down one from the upper left,and there's 1 more. Move that square 1 to the right, and there is your 4th square.
If you again start from the upper left, you can see a 2x2 square. You can use the same procedure as above to find 9 2x2 squares. Use the same process for all of the 2x2 squares
Feb 10, 2013 13:53:57 #
Feb 10, 2013 13:55:45 #
Chappy0617 wrote:
The 8 are contained in 2.
Yes. I missed the two big ones the first time, that's how I initially got 38. The two larger squares bring the total to 40.
Feb 10, 2013 15:43:37 #
If you go back to the original question, it is the key to this little quarky puzzle.
It should have read how many SQUARES can you create from.....
It should have read how many SQUARES can you create from.....
Feb 10, 2013 16:13:10 #
Bruce M. wrote:
How many can you create from this, assume square even if not perfectly square.
I assume that you are talking about squares and not rectangles..
Lets see if we can get this thing displayed so we don't have to keep downloading it to see it.
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