The only strict rule for Bongard Problems is that the exact same image can’t appear on both sides.
No solution!
However, here are some Bongard Problems that violate the spirit of Bongard Problems for other reasons.
BP solutions should not depend on the positioning of the boxes, i.e. rearranging the boxes on either side of a given BP should retain the solution.
Non-solution:
Box shown in diagram matches where box is vs. box shown in diagram doesn't match where box is.
BP solutions should not be properties about the collection of the boxes that can’t be seen in individual boxes.
Non-solution:
High variance in position between boxes vs. low variance in position between boxes.
Interpretation of a box should not depend on any other box. Each BP box would be unambiguously and correctly sorted if all other boxes were absent.
Non-solution:
Larger version of shape vs. smaller version of shape.
BP solutions should generally not reference anything specific to a certain culture. For example, this BP is described by its own right side:
Non-solution:
English words with positive connotation vs. English words with negative connotation.
A BP's solution should not be self-referential.
Non-solution:
Box that is in this Bongard Problem vs. box that isn't in this Bongard Problem.
BP solutions should be simple. In particular they should not involve long ". . . or . . . or . . . or . . ." chains. Any collection of random boxes (without repeats) admits some such convoluted solution.
Non-solution:
White triangle or large white circle or black shape with concavity on the down-left side or heptagon or partial sector of circle or hexagon vs. not that.
