# Bongardium Leviosa

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.

To make my intention clearer, here are more examples:

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

• This may be of help: bayl fgenvtug yvarf ner pbapnir, nyy fzbbgu pheirf ner pbairk. Commented Apr 26, 2018 at 2:47
• To clarify, the fourth shape on the right was changed to make it more clearly not fit the rule. Commented Apr 26, 2018 at 3:03
• I'm unsure about the lower left: For all others: zvffvat funcrf gb na fznyyrfg rapbzcnffvat pvepyr vf rknpgyl gjb Commented May 14, 2018 at 11:30

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.

• Welcome to Puzzling.SE. To avoid spoiling the puzzle for other users, please use >! to hide your answer from accidental view. Commented Apr 26, 2018 at 3:19
• Good answer! This isn't what I had in mind, but it fits the shapes I included. Commented Apr 26, 2018 at 3:23

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.

• This is incorrect. Commented Apr 26, 2018 at 12:01

Perhaps,

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

• The centre-right shape on the right has none. Commented Apr 26, 2018 at 2:33
• And the bottom-left and bottom-right shapes on the left have two. Commented Apr 26, 2018 at 2:34
• As Gareth showed, this is incorrect. Commented Apr 26, 2018 at 2:51

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

• This doesn't seem well-defined, and is not what I had in mind. Commented Apr 26, 2018 at 12:02

Every shape on the left can be stretched into a circle, but those on the right cannot.

• Welcome to Puzzling.SE! Could you explain a bit more how your answer works - especially how it works for the second set of examples? Commented May 3, 2018 at 11:59

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.

• 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 Commented Apr 26, 2018 at 16:09