8
$\begingroup$

Entering 30 characters is quite a lo

enter image description here

$\endgroup$
  • 4
    $\begingroup$ Please don't use JPG for non-photographic images. $\endgroup$ – Andreas Rejbrand Mar 15 '18 at 11:22
10
$\begingroup$

Assuming that

a pixel counts as a rectangle,

there are

14460060000 rectangles. That is the count of various sized rectangles in a grid of 600 x 400 rectangles. For example, there are $1152 = (600-589+1) \times (400-305+1)$ rectangles of size $589 \times 305$.

$\endgroup$
  • 1
    $\begingroup$ I have an LCD, so all my pixels have three(?) subpixels. Wouldn't that change the number? $\endgroup$ – Alexander Mar 15 '18 at 13:57
  • 3
    $\begingroup$ @Alexander, this is a logic puzzle, so it's fair to assume we're talking about logical pixels, not physical ones ;-) $\endgroup$ – Doctor Jones Mar 15 '18 at 14:09
7
$\begingroup$

I will say that there is:

240000 rectangles. The image is 600x400 pixels, and since squares are a kind of rectangle, I'm going to go with that. I'm thinking its going to be more complex than that though.

Updated answer:

Using a formula I found on a different question, the amount of rectangles found on a grid m wide and n tall is equal to mn(m+1)(n+1)/4. This gives us an answer of 14460060000 rectangles on a 400x600 grid.

$\endgroup$
  • 2
    $\begingroup$ That can’t be it. A group of two or four squares still forms another rectangle $\endgroup$ – ALinuxLover Mar 15 '18 at 11:13
  • 1
    $\begingroup$ Yeah, that is what I was thinking. I'm gonna try something $\endgroup$ – Shinji Wins Mar 15 '18 at 11:16
  • 2
    $\begingroup$ I know, I accidentally deleted the edit the first time too! Ill get him next time :P $\endgroup$ – Shinji Wins Mar 15 '18 at 11:27
  • 2
    $\begingroup$ All squares are rectangles, but not all rectangles are squares. So I would argue that a rectangle isn't a specialised case of a square. $\endgroup$ – Shinji Wins Mar 15 '18 at 11:30
  • 1
    $\begingroup$ @ShinjiWins well we can apply all the same formulae of a square to a rectangle, and vice versa. Say the rectangle has length $a$ and width $b$ then area is equal to $ab$. And volume is equal to $abc$ if the rectangle had some depth $c$. And surface area of a rectangle in three dimensions would be $2(ab + bc + ac)$. We can apply the same formulae to a square, but for the shape to be a square in the first place, $a = b = c$. It seems like all rectangles can be squares if we just change the sign from being $\neq$ to $=$. $\endgroup$ – Mr Pie Mar 15 '18 at 11:34
4
$\begingroup$

Well... I will say...

Zero? None of the red shapes is a real rectangle. If you focus you can see some orange rectangles flashing inside the red shapes but that is just optical illusions.

With the lateral-thinking tag I have another answer:

240 000, the total number of pixels of this image (600x400), a pixel is a square, and a square is a rectangle.

$\endgroup$
  • 1
    $\begingroup$ It's the JPG compression. One should never use JPG for non-photographic images. $\endgroup$ – Andreas Rejbrand Mar 15 '18 at 11:21
3
$\begingroup$

I think it is:

1 the image itself is a 1 giant white rectangle.

$\endgroup$
  • 1
    $\begingroup$ exactly what i thought $\endgroup$ – Mario Garcia Mar 15 '18 at 11:20
2
$\begingroup$

Combining both the answer from Shinji Wins & Mhmd, one might conclude:

It has 240001, 240000 for the amount of pixels and one for the entire picture

$\endgroup$
2
$\begingroup$

There are as many rectangles as the meaning of the question will allow. So the answer is anything between 1 (the whole image) and infinity (if we allow the set of all possible rectangles which could be fitted in the bounding rectangle).

$\endgroup$

Not the answer you're looking for? Browse other questions tagged or ask your own question.