See BP873 for comparisons based on discrete quantities vs. comparisons based on continuous quantities. All examples in that Bongard Problem fit left here.

Similar to BP200 with sides flipped. (However, "Bongard Problem based on quantity" is a more general criterion than "Bongard Problem based on discrete counting.")

See BP507 for the version with links to pages on the OEBP instead of images of Bongard Problems (miniproblems).

Adjacent-numbered pages:
BP869 BP870 BP871 BP872 BP873  *  BP875 BP876 BP877 BP878 BP879

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

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

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

Adjacent-numbered pages:
BP874 BP875 BP876 BP877 BP878  *  BP880 BP881 BP882 BP883 BP884

abstract, 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 on the left.

Adjacent-numbered pages:
BP875 BP876 BP877 BP878 BP879  *  BP881 BP882 BP883 BP884 BP885

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

bpimage_shapes [smaller | same | bigger]
zoom in left

Aaron David Fairbanks

You can try to interpret these images as Bongard Problems. This works just when the left side includes no objects that would fit in with the right side (as in EX7357 but not EX7361), the solution is "not [right pattern] vs. [right pattern]"; otherwise there is no apparent solution.

The solvable Bongard Problems sorted left here are right-narrow and not left-narrow, with the left side the negation of the right side (see notso).

Adjacent-numbered pages:
BP876 BP877 BP878 BP879 BP880  *  BP882 BP883 BP884 BP885 BP886

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

bpimage_shapes_nosoln_allowed [smaller | same | bigger]

Aaron David Fairbanks

Left-sorted Bongard Problems have the keyword "presentationmatters" on the OEBP.

Right-sorted Bongard Problems have the keyword "presentationinvariant" on the OEBP.

Meta Bongard problems that sort Bongard Problems purely based on their solutions usually have two versions in the database: one that sorts images of Bongard Problems and one that sorts links to pages on the OEBP. If both versions exist, users should make them cross-reference one another. (Meta Bongard Problems that sort images of Bongard Problems have the keyword miniproblems, whereas meta Bongard Problems that sort links to OEBP pages have the keyword links.)

For meta-pages on the OEBP that sort other pages on the OEBP (keyword links), "presentationmatters" means factoring in content like the BP number, the currently uploaded examples, the wording of the title, the description, and so on, rather than just the solution (that is, how the page would sort all potential examples). This is unusual.

"One solution vs. multiple solutions" (BP828) seems like a border-case. - Aaron David Fairbanks, Aug 01 2020

See BP1010 (projectionmatters versus 3d) for a similar idea: there 2D representations are to 3D objects as here Bongard Problems are to Bongard Problem solutions.

Adjacent-numbered pages:
BP890 BP891 BP892 BP893 BP894  *  BP896 BP897 BP898 BP899 BP900

fuzzy, meta (see left/right), links, keyword, right-self, sideless, metameta, right-it, dependence, presentationinvariant

metabp [smaller | same | bigger]

Jago Collins

All examples are Bongard Problems fitting left or right in BP793.

All examples here are in the conventional format, i.e. white background, black vertical dividing line, and examples in boxes on either side.

Border cases are Bongard Problems that always self-sort one way given their particular visual format (e.g. fixed number of boxes), but self-sort a different way in another slightly different format.

Meta Bongard Problems appearing in BP793 that are presentationinvariant necessarily fit right here.

It is interesting to think about how this Bongard Problem sorts itself. The only self-consistent answer is that it fits right.

See BP793 "sorts self left vs. sorts self right".

See BP944 "sorts every BP on one side vs. doesn't".

Adjacent-numbered pages:
BP922 BP923 BP924 BP925 BP926  *  BP928 BP929 BP930 BP931 BP932

hard, solved, presentationinvariant, visualimagination

boxes_bpimage_sorts_self [smaller | same | bigger]
zoom in left (boxes_bpimage_sorts_self_incarnation_dependent) | zoom in right

Aaron David Fairbanks