See BP567 for the version with links to pages on the OEBP instead of images of Bongard Problems (miniproblems).

Adjacent-numbered pages:
BP791 BP792 BP793 BP794 BP795  *  BP797 BP798 BP799 BP800 BP801

hard, nice, abstract, dual, handed, leftright, challenge, meta (see left/right), miniproblems, creativeexamples, assumesfamiliarity, structure, presentationinvariant

boxes_bpimage [smaller | same | bigger]

Aaron David Fairbanks

In particular, horizontal reflections work in all left examples.

An image of this Bongard Problem would fit on the left.

See BP552 for the version with links to pages on the OEBP instead of images of Bongard Problems (miniproblems).

Adjacent-numbered pages:
BP866 BP867 BP868 BP869 BP870  *  BP872 BP873 BP874 BP875 BP876

hard, abstract, challenge, meta (see left/right), miniproblems, creativeexamples, presentationmatters, infodense, assumesfamiliarity, structure

bpimage_shapes [smaller | same | bigger]

Aaron David Fairbanks

See BP553 for the version with links to pages on the OEBP instead of images of Bongard Problems (miniproblems).

Adjacent-numbered pages:
BP867 BP868 BP869 BP870 BP871  *  BP873 BP874 BP875 BP876 BP877

hard, challenge, meta (see left/right), miniproblems, creativeexamples, presentationmatters, assumesfamiliarity, structure

bpimage_shapes [smaller | same | bigger]

Aaron David Fairbanks

Left examples partition a pool of objects cleanly into two classes.

See BP509 (keyword "allsorted") for the version with links to pages on the OEBP instead of images of Bongard Problems.

The left side implies BP876^left.

Adjacent-numbered pages:
BP870 BP871 BP872 BP873 BP874  *  BP876 BP877 BP878 BP879 BP880

hard, challenge, meta (see left/right), miniproblems, creativeexamples, assumesfamiliarity, structure, presentationinvariant

bpimage_shapes [smaller | same | bigger]
zoom in left | zoom in right

Aaron David Fairbanks

Left Bongard Problems do not have to sort all relevant examples; if they would leave some border cases unsorted, it just has to be clear precisely which examples those would be.

Often a precise divide between values on a spectrum comes from intuitively "crossing a threshold." For example, there is an intuitive threshold between acute and obtuse angles. Two sides of a Bongard Problem on opposite ends of a threshold, coming close to it, are interpreted as having precise divide between sides, right up against that threshold.

See BP508 for the version with links to pages on the OEBP instead of images of Bongard Problems.

Adjacent-numbered pages:
BP871 BP872 BP873 BP874 BP875  *  BP877 BP878 BP879 BP880 BP881

hard, notso, challenge, meta (see left/right), miniproblems, creativeexamples, assumesfamiliarity, structure, presentationinvariant

bpimage_shapes [smaller | same | bigger]
zoom in left (bpimage_shapes_exact_sort)

Aaron David Fairbanks

Left examples are quantity-comparison Problems in which the dividing point on the spectrum separating the sides lands between them. Right examples are quantity-comparison Problems in which the dividing point is the entirety of one of the sides (always the left side, for clarity).

Only less-than vs. greater-than Problems may have imprecise (BP876^right) dividing point between sides.

Adjacent-numbered pages:
BP872 BP873 BP874 BP875 BP876  *  BP878 BP879 BP880 BP881 BP882

hard, challenge, meta (see left/right), miniproblems, creativeexamples, assumesfamiliarity, structure, presentationinvariant

bpimage_shapes_quantity_soln [smaller | same | bigger]

Aaron David Fairbanks

"Allsorted" Bongard Problems (BP875^left) always fit as right examples.

Left examples are never "allsorted".

Adjacent-numbered pages:
BP873 BP874 BP875 BP876 BP877  *  BP879 BP880 BP881 BP882 BP883

hard, challenge, meta (see left/right), miniproblems, creativeexamples, assumesfamiliarity, structure, presentationinvariant

bpimage_shapes_exact_sort [smaller | same | bigger]
zoom in left | zoom in right (bpimage_shapes_exact_sort_no_midway)

Aaron David Fairbanks

Loosely speaking, examples on the left are "Bongard Problems that can be self-similar". However, Bongard Problems with images of themselves deeply nested in boxes or rotated/flipped are not considered "self-similar"; the Bongard Problem must use itself, as-is (allowing downward scaling and ignoring pixelation), as a panel.

All examples here are in the conventional format, i.e. white background, black vertical dividing line, and examples in boxes on either side. (A more general version of this Bongard Problem might allow many formats of Bongard Problems, sorting an image left if a self-similar version is possible having the same solution and format. This more general version would no longer be tagged presentationinvariant, since sorting would not only depend on solution, but also format.)

It would hint at the solution (keyword help) to only include images of Bongard Problems that, as it stands, are already clearly categorized on one side by themselves. (That is, images of Bongard Problems that belong on one of the two sides of BP793.) It is tricky to come up with images that are categorized by themselves as it stands but that could NOT be recursively included within themselves. EX7967, EX7999, EX7995, and EX6574 are some examples.

See BP987 which narrows down the left-hand side of this BP further based on whether or not the BP could contain itself as a panel on both sides.

Adjacent-numbered pages:
BP949 BP950 BP951 BP952 BP953  *  BP955 BP956 BP957 BP958 BP959

hard, stub, abstract, challenge, meta (see left/right), miniproblems, infinitedetail, presentationinvariant, visualimagination

Leo Crabbe

Adjacent-numbered pages:
BP1033 BP1034 BP1035 BP1036 BP1037  *  BP1039 BP1040 BP1041 BP1042 BP1043

hard, precise, allsorted, handed, leftright, math, challenge, meta (see left/right), miniproblems, assumesfamiliarity, structure, preciseworld, presentationinvariant

boxes_dots_bpimage_clear_set_of_numbers [smaller | same | bigger]

Aaron David Fairbanks

Adjacent-numbered pages:
BP1035 BP1036 BP1037 BP1038 BP1039  *  BP1041 BP1042 BP1043 BP1044 BP1045

hard, precise, allsorted, convoluted, notso, handed, leftright, math, challenge, meta (see left/right), miniproblems, assumesfamiliarity, structure, preciseworld, presentationinvariant

boxes_dots_bpimage_clear_set_of_numbers [smaller | same | bigger]

Aaron David Fairbanks