Which is the next shape? Pick from the bottom line:

enter image description here

Source: Iranian Ph.D. university entrance exam 2017

  • 1
    $\begingroup$ This is the second of these you've posted in rapid succession. Did you create these yourself, or did you get them from somewhere online? $\endgroup$ – F1Krazy Feb 15 '18 at 16:02
  • $\begingroup$ @f1krazy They are some questions of a university entrance exam, I tried to solve but got no idea. Why? $\endgroup$ – Ahmad Feb 15 '18 at 16:08
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    $\begingroup$ I was just about to reply to your Meta post explaining this, but if you've taken a puzzle from somewhere else, you need to state this and link to the original puzzle. Depending on where you took the puzzle from, you might not actually be allowed to post it here: for example, we don't allow questions from ongoing competitions. $\endgroup$ – F1Krazy Feb 15 '18 at 16:11
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    $\begingroup$ Okay. If they're from a past exam, then that's fine, but it might be a good idea to state that at the top of the question, at the very least. $\endgroup$ – F1Krazy Feb 15 '18 at 16:19
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    $\begingroup$ @Ahmad Does the third image in the top line definitely match the original? (prompted by Hellion's answer). $\endgroup$ – hexomino Feb 16 '18 at 17:39

I'd pick...

the third shape.


- the second shape has a 2x2 section in the top left rotated clockwise,
- the third has a 2x2 section in the bottom right rotated counterclockwise,
- the 4th has a 3x3 section in the top left rotated clockwise,
- the 5th has a 3x3 section in the bottom right rotated counterclockwise
- the shape that then fits the apparent pattern is the third, which has a 4x4 section in the top left rotated clockwise.

  • $\begingroup$ This must be close. In fact, if you slightly altered the third image in the top line, it would work. $\endgroup$ – hexomino Feb 16 '18 at 17:37
  • $\begingroup$ I've been working along the exact same lines for the last day or two - and with the same lack of satisfaction in the development, or lack thereof, of a pattern in the changes. Also, having what seem to be 2 pairs of changes doesn't strongly indicate what the unknown next change (the first part of the 3rd pair) might be. $\endgroup$ – jwolf Feb 16 '18 at 19:59
  • $\begingroup$ @jwolf I answered the question, please take a look at it. $\endgroup$ – Ahmad Feb 17 '18 at 9:24
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    $\begingroup$ While the early question had a mistake, and I am so sorry for that, you actually solved it. If you consider modifying your answer according to the correct answer! I would be glad to accept it as the accepted answer! $\endgroup$ – Ahmad Feb 17 '18 at 12:37
  • $\begingroup$ @ahmad modifications made. :-) $\endgroup$ – Hellion Feb 17 '18 at 14:36

I believe the answer is:

Table 2


Row-by-row comparison of the known tables reveals that the top row has two blue blocks, the second row has one, the third row has one, the fourth has two, and the bottom has two. The second table is the only one that fits this criteria.

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    $\begingroup$ But the fifth table has three in the fourth row and only one in the bottom row. This seems mostly right, but doesn't quite hold up all the way. $\endgroup$ – DqwertyC Feb 15 '18 at 21:03
  • $\begingroup$ No! the answer is something else. $\endgroup$ – Ahmad Feb 16 '18 at 5:27
  • $\begingroup$ Ah. Somehow I glossed over the last one. No Ph.D. for me! $\endgroup$ – burtondrummerNY Feb 16 '18 at 12:32

Yes, it was a hard question.

Here is the answer; so Hellion also pointed that. However, the rotations are clockwise and anticlockwise in turn.

enter image description here

So, the answer is

The third one.

  • $\begingroup$ I'm afraid your 3rd image is different. In the question, both the lower-right 2x2 and the upper-left 2x2 seem to rotate as we move from image 2 to image 3. And then from image 3 to image 4, the upper-left moves one square to the right rather than rotating. These were both pretty fundamental problems I had with the rotational sections approach - as much as I wanted it to work. $\endgroup$ – jwolf Feb 17 '18 at 9:34
  • $\begingroup$ @jwolf I am so sorry, please forgive me. Yeah, I had a mistake in creating the puzzle... However, later I found that I can find the PDF file and copy the original puzzle from there. If I decided to post another such question, I would copy it from the original source. $\endgroup$ – Ahmad Feb 17 '18 at 10:07
  • $\begingroup$ Forgiven. Should probably let Hellion know too. $\endgroup$ – jwolf Feb 17 '18 at 10:22

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