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This was insprired by this puzzle.

This follows the rules of a classic Bongard puzzle: find the rule that all shapes on the left follow, but none of the shapes on the right do.

enter image description here

To make my intention clearer, here are more examples:

enter image description here

Assume that the third example on the left is perfectly circular outside of the two missing wedges.

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  • $\begingroup$ This may be of help: bayl fgenvtug yvarf ner pbapnir, nyy fzbbgu pheirf ner pbairk. $\endgroup$ – tox123 Apr 26 '18 at 2:47
  • $\begingroup$ To clarify, the fourth shape on the right was changed to make it more clearly not fit the rule. $\endgroup$ – Austin Weaver Apr 26 '18 at 3:03
  • $\begingroup$ I'm unsure about the lower left: For all others: zvffvat funcrf gb na fznyyrfg rapbzcnffvat pvepyr vf rknpgyl gjb $\endgroup$ – martin May 14 '18 at 11:30
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All the shapes on the left have two or less outward facing corners, but every shape on the right has more than two outward facing corners.

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    $\begingroup$ Welcome to Puzzling.SE. To avoid spoiling the puzzle for other users, please use >! to hide your answer from accidental view. $\endgroup$ – Rupert Morrish Apr 26 '18 at 3:19
  • $\begingroup$ Good answer! This isn't what I had in mind, but it fits the shapes I included. $\endgroup$ – Austin Weaver Apr 26 '18 at 3:23
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This is a little tenuous, but here goes...

Imagine each shape edge is a string, and each vertex is a hole. Then attempt to pull each string taut. Straight edges will remain the same, but curved edges will shrink until they become straight.

Then, the shapes on the left will no longer be closed shapes (either becoming points or lines). The shapes on the right remain as closed shapes.

The contentious one is the pac-man shape (left panel #2/top-right). Perhaps when pulled taut, the string follows the contour of the two existing straight lines, therefore producing a caret (not a closed shape) instead of a triangle (if you were to simply connect the vertices by straight lines). The top-left shape is also contentious; if the three vertices are not collinear, you get a closed triangle upon pulling the strings taut.

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  • $\begingroup$ This is incorrect. $\endgroup$ – Austin Weaver Apr 26 '18 at 12:01
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Perhaps,

All the left ones have only axis of symmetry, whereas on the right they have more than one axis of symmetry.

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  • $\begingroup$ The centre-right shape on the right has none. $\endgroup$ – Gareth McCaughan Apr 26 '18 at 2:33
  • $\begingroup$ And the bottom-left and bottom-right shapes on the left have two. $\endgroup$ – Gareth McCaughan Apr 26 '18 at 2:34
  • $\begingroup$ As Gareth showed, this is incorrect. $\endgroup$ – Austin Weaver Apr 26 '18 at 2:51
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My thoughts:

All shapes on the right were modified from an ellipsoid, which were pinched, fused or cut. The ones on the left evolve from a variety of shapes

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  • $\begingroup$ This doesn't seem well-defined, and is not what I had in mind. $\endgroup$ – Austin Weaver Apr 26 '18 at 12:02
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All of the shapes on the Left have a vertical line to their right, while none of the shapes on the Right do.

A stretch until I can think of another answer.

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  • $\begingroup$ The vertical line should be a separator, and not part of the puzzle; in the original version all 12 shapes are supposed to be boxed $\endgroup$ – SilverCookies Apr 26 '18 at 16:09
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Every shape on the left can be stretched into a circle, but those on the right cannot.

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    $\begingroup$ Welcome to Puzzling.SE! Could you explain a bit more how your answer works - especially how it works for the second set of examples? $\endgroup$ – puzzledPig May 3 '18 at 11:59

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