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	. . .

(edit; present; nest [left/right]; search; history; show unpublished changes)

	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	. . .

(edit; present; nest [left/right]; search; history; show unpublished changes)

	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

(edit; present; nest [left/right]; search; history; show unpublished changes)

	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`

BP592

Bongard Problem with solution relating to concept: becoming larger / becoming smaller vs. Bongard Problem unrelated to this concept.

BP43	BP74	BP108	BP179	BP180	BP278
BP286	BP300	BP318	BP341	BP350	BP351
BP352	BP357	BP365	BP1266

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

	CROSSREFS	`Adjacent-numbered pages: BP587 BP588 BP589 BP590 BP591 * BP593 BP594 BP595 BP596 BP597`
	KEYWORD	`meta (see left/right), links, metaconcept, primitive`
	CONCEPT	`This MBP is about BPs that feature concept: "size_increase_decrease"` `Searchable synonyms: "larger, becoming", "smaller, becoming", "increasing", "decreasing".`
	WORLD	`bp [smaller \| same \| bigger]`
	AUTHOR	`Harry E. Foundalis`

BP610

Bongard Problem with solution relating to concept: convex hull vs. Bongard Problem unrelated to this concept.

BP12	BP65	BP81	BP82	BP83	BP84
BP97	BP138	BP192	BP242	BP268	BP272
BP278	BP280	BP348	BP891	BP1094

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

	CROSSREFS	`Adjacent-numbered pages: BP605 BP606 BP607 BP608 BP609 * BP611 BP612 BP613 BP614 BP615`
	KEYWORD	`meta (see left/right), links, metaconcept, primitive`
	CONCEPT	`This MBP is about BPs that feature concept: "convex_hull"`
	WORLD	`bp [smaller \| same \| bigger]`
	AUTHOR	`Harry E. Foundalis`

BP658

Bongard Problem with solution relating to concept: leftward / rightward vs. Bongard Problem unrelated to this concept.

BP43

BP206

BP278

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

	CROSSREFS	`Adjacent-numbered pages: BP653 BP654 BP655 BP656 BP657 * BP659 BP660 BP661 BP662 BP663`
	KEYWORD	`meta (see left/right), links, metaconcept`
	CONCEPT	`This MBP is about BPs that feature concept: "leftward_rightward"`
	WORLD	`bp [smaller \| same \| bigger]`
	AUTHOR	`Harry E. Foundalis`

BP686

Bongard Problem with solution relating to concept: regular change / irregular change vs. Bongard Problem unrelated to this concept.

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

	CROSSREFS	`Adjacent-numbered pages: BP681 BP682 BP683 BP684 BP685 * BP687 BP688 BP689 BP690 BP691`
	KEYWORD	`meta (see left/right), links, metaconcept, primitive`
	CONCEPT	`This MBP is about BPs that feature concept: "regular_irregular_change"`
	WORLD	`bp [smaller \| same \| bigger]`
	AUTHOR	`Harry E. Foundalis`

BP708

Bongard Problem with solution relating to concept: tracing along a line or curve vs. Bongard Problem unrelated to this concept.

BP16	BP43	BP52	BP55	BP67	BP68
BP69	BP70	BP72	BP74	BP102	BP105
BP115	BP120	BP179	BP180	BP198	BP208
BP278	BP336	BP340	BP341	BP350	BP351
BP352	BP353	BP354	BP355	BP356	BP357
BP363	BP365

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

	CROSSREFS	`Adjacent-numbered pages: BP703 BP704 BP705 BP706 BP707 * BP709 BP710 BP711 BP712 BP713`
	KEYWORD	`meta (see left/right), links, metaconcept, primitive`
	CONCEPT	`This MBP is about BPs that feature concept: "tracing_line_or_curve"`
	WORLD	`bp [smaller \| same \| bigger]`
	AUTHOR	`Harry E. Foundalis`

BP1194

Bongard Problems listed in Harry E. Foundalis's collection vs. not.

BP1	BP2	BP3	BP4	BP5	BP6
BP7	BP8	BP9	BP10	BP11	BP12
BP13	BP14	BP15	BP16	BP17	BP18
BP19	BP20	BP21	BP22	BP23	BP24
BP25	BP26	BP27	BP28	BP29	BP30
BP31	BP32	BP33	BP34	BP35	. . .

	BP501	BP503	BP504	BP505	BP506	BP507
	BP508	BP509	BP510	BP1194

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

	COMMENTS	`Alternatively, BP pages on the OEBP with number less than or equal to 394 vs. other BP pages.`
	REFERENCE	`https://www.foundalis.com/res/bps/bpidx.htm`
	CROSSREFS	`Adjacent-numbered pages: BP1189 BP1190 BP1191 BP1192 BP1193 * BP1195 BP1196 BP1197 BP1198 BP1199`
	EXAMPLE	`Foundalis's collection includes all Bongard Problems by Bongard.`
	KEYWORD	`meta (see left/right), links, right-self, time`
	AUTHOR	`Aaron David Fairbanks`

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