The On-Line Encyclopedia of Bongard Problems

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Bongard Problems by Bongard vs. other Bongard Problems.

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	. . .

BP101	BP102	BP103	BP104	BP105	BP106
BP107	BP108	BP109	BP110	BP111	BP112
BP113	BP114	BP115	BP116	BP117	BP118
BP119	BP120	BP121	BP122	BP123	BP124
BP125	BP126	BP127	BP128	BP129	BP130
BP131	BP132	BP133	BP134	BP135	. . .

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	COMMENTS	`Alternatively, BP pages on the OEBP with number less than or equal to 100 vs. other BP pages.` `Bongard's original Problems have the keyword "bongard" on the OEBP.`
	CROSSREFS	`Adjacent-numbered pages: BP793 BP794 BP795 BP796 BP797 * BP799 BP800 BP801 BP802 BP803`
	KEYWORD	`meta (see left/right), links, keyword`
	WORLD	`bppage [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP797

Image conceptually relates to the golden ratio/Fibonacci numbers versus not so.

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	CROSSREFS	`BP800 is the metaconcept page for this concept.` `Adjacent-numbered pages: BP792 BP793 BP794 BP795 BP796 * BP798 BP799 BP800 BP801 BP802`
	KEYWORD	`abstract, math, concept, experimental`
	CONCEPT	`golden_ratio (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP796

Image of a Bongard Problem that would sort a blank panel on its left versus image of a Bongard Problem that would sort a blank panel on its right.

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	CROSSREFS	`See BP567 for the version with links to pages on the OEBP instead of images of Bongard Problems (miniproblems).` `Adjacent-numbered pages: BP791 BP792 BP793 BP794 BP795 * BP797 BP798 BP799 BP800 BP801`
	KEYWORD	`hard, nice, abstract, dual, handed, leftright, challenge, meta (see left/right), miniproblems, creativeexamples, assumesfamiliarity, structure, presentationinvariant`
	WORLD	`boxes_bpimage [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP795

Image of a Bongard Problem that would sort itself on its own right versus image of a Bongard Problem that would sort itself on its own left.

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	COMMENTS	`"BONGARD HELL."` `This the flipped version of BP793 but using only images of Bongard Problems with solution "__ half more black/less white than other half versus vice versa," that all use rotated, reflected, and inverted versions of the same examples.`
	CROSSREFS	`See BP971 (left vs. right more black) and BP972 (top vs. bottom more black).` `Adjacent-numbered pages: BP790 BP791 BP792 BP793 BP794 * BP796 BP797 BP798 BP799 BP800`
	KEYWORD	`hard, nice, abstract, dual, handed, leftright, meta (see left/right), miniproblems, presentationmatters, left-finite, right-finite, assumesfamiliarity, structure, experimental, funny`
	WORLD	`bongard_hell [smaller \| same \| bigger] zoom in left \| zoom in right`
	AUTHOR	`Aaron David Fairbanks`

BP794

Meta Bongard Problems that can contain an infinite chain of Bongard Problems containing Bongard Problems vs. this can never happen.

BP794

BP1073

BP552	BP553	BP554	BP556	BP567	BP572
BP838	BP913	BP958	BP976	BP995	BP1079
BP1081

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	COMMENTS	`Right examples have the keyword "wellfounded" on the OEBP.` `This BP is not wellfounded, but its right side is. A paradoxical BP would be "Meta Bongard Problems that can contain an infinite chain of Bongard Problems containing Bongard Problems on the right side vs. this can never happen": where does it sort itself?`
	CROSSREFS	`left-self or right-self implies not wellfounded.` `Wellfounded implies not feedback.` `Adjacent-numbered pages: BP789 BP790 BP791 BP792 BP793 * BP795 BP796 BP797 BP798 BP799`
	KEYWORD	`meta (see left/right), links, keyword, left-self, metameta, left-it, feedback`
	CONCEPT	`recursion (info \| search)`
	WORLD	`linksbp [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP793

Image of a Bongard Problem that would sort itself on its own left versus image of a Bongard Problem that would sort itself on its own right.

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	COMMENTS	`Rhetorical question: Where does this Bongard Problem sort an image of itself?` `See BP999 and BP1004 for similar paradoxes.` `Bongard Problems fitting left here evidently come in three categories: 1) would sort all Bongard Problems with the same solution left, 2) would sort all Bongard Problems with the same solution right, or 3) would sort some Bongard Problems with the same solution left and some right. See BP927.`
	CROSSREFS	`See BP517 for the version with links to pages on the OEBP instead of images of Bongard Problems (miniproblems).` `See BP954, which is about Bongard Problems not only sorting themselves, but moreover fractally appearing in themselves as panels.` `Adjacent-numbered pages: BP788 BP789 BP790 BP791 BP792 * BP794 BP795 BP796 BP797 BP798`
	KEYWORD	`hard, nice, abstract, dual, handed, leftright, solved, meta (see left/right), miniproblems, creativeexamples, presentationmatters, assumesfamiliarity, structure, experimental`
	WORLD	`boxes_bpimage_sorts_self [smaller \| same \| bigger] zoom in left (boxes_bpimage_sorts_self_left) \| zoom in right (boxes_bpimage_sorts_self_right)`
	AUTHOR	`Aaron David Fairbanks`

BP792

Complete finite collection versus incomplete infinite collection.

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	COMMENTS	`Related to BP379 and BP380.` `EX10061 can ambiguously be taken to be self-referential as the set of left-hand examples (which would make the right hand solution only "incomplete sets") or the class of finite sets.`
	CROSSREFS	`Adjacent-numbered pages: BP787 BP788 BP789 BP790 BP791 * BP793 BP794 BP795 BP796 BP797`
	KEYWORD	`abstract, creativeexamples, rules, miniworlds, collection`
	CONCEPT	`completeness (info \| search),` `finite_infinite (info \| search)`
	WORLD	`collection_of_objects_same_type [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP791

The leftmost two angles measured from thin line add to the rightmost versus no two angles add to a third.

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	COMMENTS	`This answer is independent of whether angles are measured clockwise or counter-clockwise; only a consistent choice must be made.`
	CROSSREFS	`Adjacent-numbered pages: BP786 BP787 BP788 BP789 BP790 * BP792 BP793 BP794 BP795 BP796`
	KEYWORD	`math, structure, orderedtriplet, traditional`
	CONCEPT	`addition (info \| search),` `2_inputs_1_output (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP790

The leftmost two add (as vectors) to the right versus no two add to a third.

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	CROSSREFS	`Adjacent-numbered pages: BP785 BP786 BP787 BP788 BP789 * BP791 BP792 BP793 BP794 BP795`
	KEYWORD	`math, structure, orderedtriplet, traditional`
	CONCEPT	`addition (info \| search),` `2_inputs_1_output (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP789

Bongard Problems in which all examples have the same format, a specific multi-part structure vs. other Bongard Problems.

BP200	BP324	BP325	BP339	BP346	BP350
BP351	BP352	BP353	BP354	BP355	BP356
BP357	BP361	BP362	BP372	BP548	BP790
BP791	BP793	BP795	BP796	BP802	BP803
BP805	BP827	BP828	BP829	BP831	BP832
BP833	BP834	BP835	BP836	BP843	. . .

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	COMMENTS	`Left examples have the keyword "structure" on the OEBP.` `Examples of "structures": Bongard Problem, Bongard Problem with extra unsorted panel ("Bongard's Dozen"), 4-panel analogy grid, sequence of objects with a quantity changing by a constant amount.` `If the solver hasn't become familiar with the featured structure, the Bongard Problem's solution may seem convoluted or inelegant. (See keyword assumesfamiliarity.) Once the solver gets used to seeing a particular structure it becomes easier to read that structure and solve Bongard Problems featuring it.` `A Bongard Problem can non-verbally teach someone how a particular structure works, showing valid examples of that structure versus non-examples. E.g., BP968 for the structure of Bongard Problems and BP981 for the structure of analogy grids.`
	CROSSREFS	`Adjacent-numbered pages: BP784 BP785 BP786 BP787 BP788 * BP790 BP791 BP792 BP793 BP794`
	KEYWORD	`meta (see left/right), links, keyword`
	WORLD	`bp [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

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