The On-Line Encyclopedia of Bongard Problems

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Image of Bongard Problem that would sort ANY image of a valid Bongard Problem on one of its sides vs. image of Bongard Problem whose categorization of a BP image would depend on the solution or examples in it.

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	COMMENTS	`"Any" here means any image of a Bongard Problem in the relevant format, i.e. with white background, black vertical dividing line, and examples in boxes on either side.` `All examples shown in this Problem clearly sort themselves on the left or right.` `A self-referential but maybe simpler solution is "would sort all examples in this whole Bongard Problem on one of its sides vs. not so." Users adding examples please try to maintain this: for any example you add to the right of this Bongard Problem, make sure it does not sort all the other examples in this Bongard Problem on just one of its sides. - Aaron David Fairbanks, Aug 26 2020`
	CROSSREFS	`Adjacent-numbered pages: BP939 BP940 BP941 BP942 BP943 * BP945 BP946 BP947 BP948 BP949`
	KEYWORD	`hard, challenge, presentationinvariant`
	WORLD	`boxes_bpimage_sorts_self [smaller \| same \| bigger] zoom in left \| zoom in right`
	AUTHOR	`Jago Collins`

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`

BP952

Images of Bongard Problems about images of Bongard Problems about images of Bongard Problems vs. images of Bongard Problems not including images of Bongard Problems including images of Bongard Problems.

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	CROSSREFS	`See BP547 for the version with links to pages on the OEBP instead of images of Bongard Problems (miniproblems).` `Any left example in this BP will be a left example for BP1084.` `Adjacent-numbered pages: BP947 BP948 BP949 BP950 BP951 * BP953 BP954 BP955 BP956 BP957`
	KEYWORD	`meta (see left/right), miniproblems, funny, presentationinvariant`
	CONCEPT	`recursion (info \| search)`
	WORLD	`[smaller \| same \| bigger] zoom in left`
	AUTHOR	`Leo Crabbe`

BP954

Solution could appear in a Bongard Problem that has itself as a panel vs. not so.

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	COMMENTS	`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 here considered "self-similar"; the Bongard Problem must use itself, as-is (allowing downward scaling and allowing infinite detail, ignoring pixelation--see keyword infinitedetail), as a panel.` `Bongard Problems fitting left evidently come in three categories: 1) the Bongard Problem could only appear on its own left side, 2) the Bongard Problem could appear on its own right side, or 3) the Bongard Problem could appear on its own left or the right side. See BP987.` `Meta Bongard Problems appearing in BP793 that are presentationinvariant necessarily fit left here.` `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.`
	CROSSREFS	`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`
	KEYWORD	`hard, abstract, challenge, meta (see left/right), miniproblems, infinitedetail, presentationinvariant, visualimagination`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search)`
	AUTHOR	`Leo Crabbe`

BP987

Solution could appear in a Bongard Problem featuring an image of itself on either of its sides vs. solution can appear in a Bongard Problem featuring an image of itself on a certain side only.

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	COMMENTS	`All examples are Bongard Problems fitting left in BP954.` `This is very close to BP927, specialized to Bongard Problems fitting left in BP954. The difference is that a Bongard Problem solution would fit left in BP927 but right here if it can sort images of it on both sides, but it is impossible to make an image of it fractally including itself on a certain side. An example is EX7997.` `Meta Bongard Problems appearing in BP793 that are presentationinvariant necessarily fit right here.`
	CROSSREFS	`Adjacent-numbered pages: BP982 BP983 BP984 BP985 BP986 * BP988 BP989 BP990 BP991 BP992`
	KEYWORD	`abstract, meta (see left/right), miniproblems, creativeexamples, assumesfamiliarity, structure, presentationinvariant, visualimagination`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search)`
	AUTHOR	`Leo Crabbe`

BP1024

One sorted left vs. one sorted right.

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	CROSSREFS	`Adjacent-numbered pages: BP1019 BP1020 BP1021 BP1022 BP1023 * BP1025 BP1026 BP1027 BP1028 BP1029`
	KEYWORD	`precise, allsorted, dual, handed, leftright, math, meta (see left/right), miniproblems, assumesfamiliarity, structure, preciseworld, presentationinvariant`
	WORLD	`boxes_dots_bpimage_clear_set_of_numbers [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1025

Two consecutive numbers sorted left vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP1020 BP1021 BP1022 BP1023 BP1024 * BP1026 BP1027 BP1028 BP1029 BP1030`
	KEYWORD	`precise, allsorted, notso, handed, leftright, math, meta (see left/right), miniproblems, assumesfamiliarity, structure, preciseworld, presentationinvariant`
	WORLD	`boxes_dots_bpimage_clear_set_of_numbers [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1026

Not an inequality solution vs. inequality solution.

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	CROSSREFS	`Adjacent-numbered pages: BP1021 BP1022 BP1023 BP1024 BP1025 * BP1027 BP1028 BP1029 BP1030 BP1031`
	KEYWORD	`precise, allsorted, math, meta (see left/right), miniproblems, assumesfamiliarity, structure, preciseworld, presentationinvariant`
	WORLD	`boxes_dots_bpimage_clear_set_of_numbers [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1027

Solution is "one dot vs. more than one dot" vs. other solution.

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	CROSSREFS	`Adjacent-numbered pages: BP1022 BP1023 BP1024 BP1025 BP1026 * BP1028 BP1029 BP1030 BP1031 BP1032`
	KEYWORD	`precise, allsorted, notso, arbitrary, handed, leftright, meta (see left/right), miniproblems, assumesfamiliarity, structure, preciseworld, presentationinvariant`
	WORLD	`boxes_dots_bpimage_clear_set_of_numbers [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1028

An even number is the least sorted left vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP1023 BP1024 BP1025 BP1026 BP1027 * BP1029 BP1030 BP1031 BP1032 BP1033`
	KEYWORD	`precise, allsorted, notso, handed, leftright, math, meta (see left/right), miniproblems, assumesfamiliarity, structure, preciseworld, presentationinvariant`
	WORLD	`boxes_dots_bpimage_clear_set_of_numbers [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

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