The On-Line Encyclopedia of Bongard Problems

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BP874

Solution is a quantity comparison vs. solution does not involve quantity.

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	CROSSREFS	`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`
	KEYWORD	`meta (see left/right), miniproblems, creativeexamples, assumesfamiliarity, structure, presentationinvariant`
	WORLD	`bpimage_shapes [smaller \| same \| bigger] zoom in left (bpimage_shapes_quantity_soln)`
	AUTHOR	`Aaron David Fairbanks`

BP875

Bongard Problem would sort all relevant examples vs. possible objects similar to those seen on both sides would have no clear sorting.

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	COMMENTS	`Left examples partition a pool of objects cleanly into two classes.`
	CROSSREFS	`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`
	KEYWORD	`hard, challenge, meta (see left/right), miniproblems, creativeexamples, assumesfamiliarity, structure, presentationinvariant`
	WORLD	`bpimage_shapes [smaller \| same \| bigger] zoom in left \| zoom in right`
	AUTHOR	`Aaron David Fairbanks`

BP876

Precise sorting of potential examples vs. not so.

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	COMMENTS	`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.`
	CROSSREFS	`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`
	KEYWORD	`hard, notso, challenge, meta (see left/right), miniproblems, creativeexamples, assumesfamiliarity, structure, presentationinvariant`
	WORLD	`bpimage_shapes [smaller \| same \| bigger] zoom in left (bpimage_shapes_exact_sort)`
	AUTHOR	`Aaron David Fairbanks`

BP877

"Less than vs. greater than" (or vice versa) vs. "equal to vs. greater than" (or less than).

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	COMMENTS	`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.`
	CROSSREFS	`Adjacent-numbered pages: BP872 BP873 BP874 BP875 BP876 * BP878 BP879 BP880 BP881 BP882`
	KEYWORD	`hard, challenge, meta (see left/right), miniproblems, creativeexamples, assumesfamiliarity, structure, presentationinvariant`
	WORLD	`bpimage_shapes_quantity_soln [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP878

Some object(s) fit precisely between the sides vs. there is no object fitting between the sides.

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	COMMENTS	`"Allsorted" Bongard Problems (BP875^left) always fit as right examples.` `Left examples are never "allsorted".`
	CROSSREFS	`Adjacent-numbered pages: BP873 BP874 BP875 BP876 BP877 * BP879 BP880 BP881 BP882 BP883`
	KEYWORD	`hard, challenge, meta (see left/right), miniproblems, creativeexamples, assumesfamiliarity, structure, presentationinvariant`
	WORLD	`bpimage_shapes_exact_sort [smaller \| same \| bigger] zoom in left \| zoom in right (bpimage_shapes_exact_sort_no_midway)`
	AUTHOR	`Aaron David Fairbanks`

BP879

Solution involves one absolute quantity vs. solution involves relative quantity (comparing two quantities).

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	CROSSREFS	`Adjacent-numbered pages: BP874 BP875 BP876 BP877 BP878 * BP880 BP881 BP882 BP883 BP884`
	KEYWORD	`abstract, meta (see left/right), miniproblems, creativeexamples, assumesfamiliarity, structure, presentationinvariant`
	WORLD	`bpimage_shapes_quantity_soln [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP880

Non-overlapping sides (patterns are disjoint) vs. possible object(s) could fit in overlap of sides (patterns intersect).

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	COMMENTS	`"Allsorted" Bongard Problems (BP875^left) always fit on the left.`
	CROSSREFS	`Adjacent-numbered pages: BP875 BP876 BP877 BP878 BP879 * BP881 BP882 BP883 BP884 BP885`
	KEYWORD	`abstract, meta (see left/right), miniproblems, creativeexamples, assumesfamiliarity, structure, presentationinvariant`
	WORLD	`bpimage_shapes [smaller \| same \| bigger] zoom in left`
	AUTHOR	`Aaron David Fairbanks`

BP881

Right pattern is proper subset of left pattern vs. right pattern is not subset of left pattern.

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	COMMENTS	`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).`
	CROSSREFS	`Adjacent-numbered pages: BP876 BP877 BP878 BP879 BP880 * BP882 BP883 BP884 BP885 BP886`
	KEYWORD	`abstract, handed, leftright, meta (see left/right), miniproblems, creativeexamples, assumesfamiliarity, structure, presentationinvariant`
	WORLD	`bpimage_shapes_nosoln_allowed [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP894

Examples fit solution (once it is known) relatively obviously vs. examples fit solution in subtle or complex, harder-to-see ways.

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	COMMENTS	`One left and one right example with each solution are shown for help.` `This BP is fuzzy for multiple reasons. How obvious it is that an example fits a rule is subjective. Also, somebody could read the simplicity of all included examples as part of a Bongard Problem's solution. For example, the more obvious version of "square number of dots vs. non-square number of dots" could be interpreted as "square small number of dots arranged in easy-to-read way vs. non-square small number of dots arranged in easy-to-read way."` `Whether this Bongard Problem solution would categorize an image of itself left or right depends on the difficulty of the solutions of the mini-Problems.`
	CROSSREFS	`See keyword help.` `See keyword hardsort.` `Adjacent-numbered pages: BP889 BP890 BP891 BP892 BP893 * BP895 BP896 BP897 BP898 BP899`
	KEYWORD	`fuzzy, abstract, notso, subjective, meta (see left/right), miniproblems, creativeexamples, presentationmatters, assumesfamiliarity, structure, contributepairs`
	WORLD	`boxes_bpimage_three_per_side [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP948

Image of Bongard Problem such that pixel-inverting examples flips the solution vs. image of Bongard Problem such that pixel-inverting examples leaves the solution invariant.

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	CROSSREFS	`See BP556 (keyword blackwhite) for the version with links to pages on the OEBP instead of images of Bongard Problems.` `Adjacent-numbered pages: BP943 BP944 BP945 BP946 BP947 * BP949 BP950 BP951 BP952 BP953`
	KEYWORD	`meta (see left/right), miniproblems, presentationinvariant`
	CONCEPT	`black_white_inversion (info \| search)`
	AUTHOR	`Leo Crabbe`

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