The On-Line Encyclopedia of Bongard Problems

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Bongard Problems such that potential left examples can intuitively be put in bijection with potential right examples vs. other Bongard Problems.

BP7	BP8	BP19	BP36	BP43	BP45
BP54	BP55	BP63	BP64	BP67	BP95
BP106	BP109	BP157	BP158	BP180	BP196
BP197	BP211	BP234	BP278	BP279	BP286
BP313	BP337	BP357	BP363	BP372	BP513
BP514	BP515	BP516	BP517	BP793	. . .

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	COMMENTS	`This is the keyword "dual" on the OEBP.` `Given an example there is some way to "flip sides" by altering it. The left-to-right and right-to-left transformations should be inverses.` `It is not required that there only be one such transformation. For example, for many handed Bongard Problem, flipping an example over any axis will reliably switch its sorting.` `It is not required that every left example must have its corresponding right example uploaded on the OEBP nor vice versa. See the keyword contributepairs for the BPs the OEBP advises users upload left and right examples for in pairs.`
	CROSSREFS	`Adjacent-numbered pages: BP529 BP530 BP531 BP532 BP533 * BP535 BP536 BP537 BP538 BP539`
	KEYWORD	`meta (see left/right), links, keyword, sideless`
	WORLD	`bp [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP535

Visual Bongard Problems such that flipping over the vertical axis (left/right) can switch an example's side vs. visual Bongard Problems whose examples' sorting doesn't change under such a transformation.

BP8	BP43	BP67	BP109	BP207	BP234
BP278	BP279	BP313	BP337	BP357	BP363
BP372	BP793	BP795	BP796	BP805	BP830
BP881	BP931	BP955	BP961	BP971	BP1008
BP1014	BP1024	BP1025	BP1027	BP1028	BP1029
BP1030	BP1031	BP1032	BP1033	BP1034	. . .

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	COMMENTS	`Left examples have the keyword "leftright" on the OEBP.`
	CROSSREFS	`See updown.` `All "leftright" Bongard Problems are handed.` `Adjacent-numbered pages: BP530 BP531 BP532 BP533 BP534 * BP536 BP537 BP538 BP539 BP540`
	KEYWORD	`meta (see left/right), links, keyword, sideless, invariance`
	WORLD	`handed_visualbp [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP552

Orientation-dependent Bongard Problems vs. orientation-independent visual Bongard Problems.

BP7	BP8	BP16	BP36	BP43	BP54
BP55	BP63	BP67	BP106	BP109	BP199
BP207	BP234	BP278	BP279	BP286	BP313
BP337	BP363	BP372	BP793	BP795	BP796
BP805	BP830	BP881	BP896	BP931	BP955
BP961	BP971	BP972	BP1008	BP1014	. . .

	BP1	BP2	BP3	BP4	BP5	BP6
	BP986	BP1197	BP1199	BP1200

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	COMMENTS	`Left examples have the keyword "handed" on the OEBP.` `If mirroring any example along the any axis can change its sorting the BP is "handed."` `Note that BPs about comparing orientation between multiple things in one example fit on the right side.`
	CROSSREFS	`See BP871 for the version with pictures of Bongard Problems (miniproblems) instead of links to pages on the OEBP.` `The keyword leftright is specifically about flipping over the vertical axis, while the keyword updown is specifically about flipping over the horizontal axis.` `Bongard Problems tagged rotate are usually "handed", since any rotation can be created by two reflections. Not necessarily, however, since the reflected step in between might not be sorted on either side by the Bongard Problem.` `Adjacent-numbered pages: BP547 BP548 BP549 BP550 BP551 * BP553 BP554 BP555 BP556 BP557`
	KEYWORD	`meta (see left/right), links, keyword, invariance, wellfounded`
	WORLD	`visualbp [smaller \| same \| bigger] zoom in left (handed_visualbp)`
	AUTHOR	`Aaron David Fairbanks`

BP572

Physical Bongard Problems vs. other visual Bongard Problems

BP199	BP234	BP273	BP274	BP336	BP358
BP536	BP551	BP850	BP896	BP933	BP1016
BP1095

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	COMMENTS	`Left examples have the keyword "physics" on the OEBP. These are visual Bongard Problems that are most easily recognized by people as depicting some physics-related phenomenon. Usually, since physics is described by mathematics, this means there is also a (perhaps complicated) solution that can be described in terms of pure geometry.`
	CROSSREFS	`See also keyword math.` `Adjacent-numbered pages: BP567 BP568 BP569 BP570 BP571 * BP573 BP574 BP575 BP576 BP577`
	KEYWORD	`meta (see left/right), links, keyword, wellfounded`
	WORLD	`visualbp [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP596

Bongard Problem with solution relating to concept: box (of Bongard Problem) vs. Bongard Problem unrelated to this concept.

	BP8	BP157	BP209	BP234	BP257	BP321
	BP818	BP933	BP942

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	CROSSREFS	`Adjacent-numbered pages: BP591 BP592 BP593 BP594 BP595 * BP597 BP598 BP599 BP600 BP601`
	KEYWORD	`meta (see left/right), links, metaconcept, primitive`
	CONCEPT	`This MBP is about BPs that feature concept: "bounding_box"`
	WORLD	`bp [smaller \| same \| bigger]`
	AUTHOR	`Harry E. Foundalis`

BP625

Bongard Problem with solution relating to concept: downward / upward vs. Bongard Problem unrelated to this concept.

	BP179	BP199	BP206	BP215	BP234	BP273
	BP274	BP286	BP337

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	CROSSREFS	`Adjacent-numbered pages: BP620 BP621 BP622 BP623 BP624 * BP626 BP627 BP628 BP629 BP630`
	KEYWORD	`meta (see left/right), links, metaconcept`
	CONCEPT	`This MBP is about BPs that feature concept: "downward_upward"`
	WORLD	`bp [smaller \| same \| bigger]`
	AUTHOR	`Harry E. Foundalis`

BP657

Bongard Problem with solution relating to concept: left / right vs. Bongard Problem unrelated to this concept.

	BP8	BP63	BP67	BP68	BP191	BP234
	BP279	BP280	BP339

(edit; present; nest [left/right]; search; history)

	CROSSREFS	`Adjacent-numbered pages: BP652 BP653 BP654 BP655 BP656 * BP658 BP659 BP660 BP661 BP662`
	KEYWORD	`meta (see left/right), links, metaconcept, primitive`
	CONCEPT	`This MBP is about BPs that feature concept: "left_right"`
	WORLD	`bp [smaller \| same \| bigger]`
	AUTHOR	`Harry E. Foundalis`

BP734

Bongard Problem with solution relating to concept: absolute direction of line vs. Bongard Problem unrelated to this concept.

(edit; present; nest [left/right]; search; history)

	CROSSREFS	`Adjacent-numbered pages: BP729 BP730 BP731 BP732 BP733 * BP735 BP736 BP737 BP738 BP739`
	KEYWORD	`meta (see left/right), links, metaconcept`
	CONCEPT	`This MBP is about BPs that feature concept: "line_absolute_direction"`
	WORLD	`bp [smaller \| same \| bigger]`
	AUTHOR	`Harry E. Foundalis`

BP737

Bongard Problem with solution relating to concept: absolute direction with respect to the bounding box vs. Bongard Problem unrelated to this concept.

	BP199	BP206	BP215	BP234	BP238	BP273
	BP274

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	CROSSREFS	`primitive` `Adjacent-numbered pages: BP732 BP733 BP734 BP735 BP736 * BP738 BP739 BP740 BP741 BP742`
	KEYWORD	`meta (see left/right), links, metaconcept`
	CONCEPT	`This MBP is about BPs that feature concept: "absolute_direction"`
	WORLD	`bp [smaller \| same \| bigger]`
	AUTHOR	`Harry E. Foundalis`

BP742

Bongard Problem with solution relating to concept: imagined motion vs. Bongard Problem unrelated to this concept.

BP175	BP201	BP234	BP239	BP323	BP336
BP358	BP369	BP370	BP376	BP389	BP850
BP856	BP933	BP1016	BP1130

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	CROSSREFS	`Adjacent-numbered pages: BP737 BP738 BP739 BP740 BP741 * BP743 BP744 BP745 BP746 BP747`
	KEYWORD	`meta (see left/right), links, metaconcept`
	CONCEPT	`This MBP is about BPs that feature concept: "imagined_motion"`
	WORLD	`bp [smaller \| same \| bigger]`
	AUTHOR	`Harry E. Foundalis`

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