Can anyone help me solve this puzzle?
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The answer is:
If you rotate the hexagon which contains $6$ middle figures counter-clockwise for $60$ degrees, you can see that each of the figures in the middle will be the half-right of its outer figure. The half-left is its mirror.
C is the right answer. It is a common error in creating "wrong" answers to derive wrong answers by changing just a bit of the correct answer for most of the answers. This seems to make it more difficult, but in fact, it makes it more easier to guess the correct solution.
To explain this in detail:
"A" is the only one depicting a simple form. All others are more complex. So "A" is improbable. Apart from "A", "E" is the only one not consisting of six little squares, but only four. So we ignore "E" as well. "B" is the only one that is not symmetric. Drop this as well. "D" is the only one upside down. This leaves "C" as the only one that has no unique difference to the rest, which makes it the correct answer with high probability.
The answer is:
Reasoning: Step 1
Most image in their original position have a vertical symmetry axis in their middle. So you rotate them either left or right 90 degrees and mirror them where their top side used to be. At this point it could be either C or D depending on the rotation direction.
This is an hexagram: a compound of 12 triangles, 6 outward-oriented and 6 inward-oriented (forming an hexagon).
For each outward-oriented triangle, there can be an uniform transformation that matches the image of an inward-oriented triangle. First, take the right vertex of the base of the top outward-oriented triangle, rotate counter-clockwise 120 degrees around this point; divide the figure inside (for instance, the ovale) in 2 symmetrical parts through its horizontal axis, keep the bottom part and mirror it on its vertical axis (no change here for the ovale). Repeat the transformation for each outward triangle, in clockwise direction: next is the rectangle, then the irregular hexagon, your missing piece, trapezoid, lozenge (knowing that the rotation axis will always be the next vertex on the hexagon). So now we are looking at the L shape figure in the hexagon: it’s the one related to our missing piece. Conversely, mirror this L shape on its vertical axis, mirror it again horizontally and keep both parts; rotate clockwise 120 degrees: the missing piece is the U shape (third image from the top among the possible solutions).
I'll add this as my thought pattern was different as far as I can tell from the other answers. You can simply:
Take each shape in a star point, rotate it clockwise 90 degrees, then chop the top half off.
The result of that operation is the inner symbol one triangle clockwise.
I figured this out starting with the trapezium as that's the only non-symmetric shape, so governs which part of the shape is taken.
With this operation, there is only one option that fits the bill.
Therefore the middle one, C, is the answer