The On-Line Encyclopedia of Bongard Problems

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Rotation-dependent Bongard Problems vs. rotation-independent visual Bongard Problems.

BP7	BP19	BP36	BP65	BP95	BP106
BP152	BP158	BP199	BP273	BP523	BP551
BP971	BP1014	BP1086	BP1087	BP1213	BP1215
BP1216	BP1218	BP1245	BP1271

BP16

BP54

BP1122

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

	COMMENTS	`Left examples have the keyword "rotate" on the OEBP.` `If rotating an example about the center can change its sorting the BP is a left example here.` `Note that BPs about relative rotation comparisons fit on the right side.`
	CROSSREFS	`See BP872 for the version with pictures of Bongard Problems instead (miniproblems) of links to pages on the OEBP.` `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: BP548 BP549 BP550 BP551 BP552 * BP554 BP555 BP556 BP557 BP558`
	KEYWORD	`notso, meta (see left/right), links, keyword, invariance, wellfounded`
	WORLD	`visualbp [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP554

Size-dependent Bongard Problems vs. size-independent visual Bongard Problems.

BP2

BP14

BP1122

BP38

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

	COMMENTS	`Left examples have the keyword "size" on the OEBP.` `If applying a scaling to the whole of any example can change its sorting the BP fits on the left side here. (For BPs with bounding boxes means scaling an object appearing in a box within the bounding box.)` `Note that BPs about relative size comparisons of multiple objects fit on the right side.`
	CROSSREFS	`Adjacent-numbered pages: BP549 BP550 BP551 BP552 BP553 * BP555 BP556 BP557 BP558 BP559`
	KEYWORD	`meta (see left/right), links, keyword, invariance, wellfounded`
	WORLD	`visualbp [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP555

Black and white photograph versus drawing.

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

	COMMENTS	`Although the images here are related to culture (BP521^left), the solution of this Bongard Problem is about the visual style of the images.`
	CROSSREFS	`Adjacent-numbered pages: BP550 BP551 BP552 BP553 BP554 * BP556 BP557 BP558 BP559 BP560`
	KEYWORD	`culture, experimental`
	WORLD	`zoom in left (black_and_white_photograph)`
	AUTHOR	`Aaron David Fairbanks`

BP556

Visual Bongard Problems such that if black and white are switched some examples switch sides vs. visual Bongard Problems that would always sort two switched versions the same way.

	BP157	BP196	BP211	BP337	BP859	BP962
	BP971	BP972	BP1008	BP1161	BP1249	BP1252

	BP170	BP359	BP524	BP1089	BP1093	BP1210
	BP1230

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

	COMMENTS	`Left-sorted examples have the keyword "blackwhite" on the OEBP.` `Right-sorted examples have the keyword "blackwhiteinvariant" on the OEBP.` `All examples are visual Bongard Problems that allow black to touch the bounding box (keyword bordercontent).`
	CROSSREFS	`Adjacent-numbered pages: BP551 BP552 BP553 BP554 BP555 * BP557 BP558 BP559 BP560 BP561`
	KEYWORD	`meta (see left/right), links, keyword, invariance, wellfounded`
	CONCEPT	`black_white_inversion (info \| search)`
	WORLD	`visualbp [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP557

Equal horizontal length vs. not

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

	COMMENTS	`All examples in this Problem are pairs of straight line segments.` `This problem communicates the idea of projected distance, in this case from 2D to 1D (x-axis).`
	CROSSREFS	`Adjacent-numbered pages: BP552 BP553 BP554 BP555 BP556 * BP558 BP559 BP560 BP561 BP562`
	KEYWORD	`nice, precise, allsorted, stretch, perfect, unorderedpair, preciseworld`
	CONCEPT	`projection (info \| search)`
	WORLD	`two_segments [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP558

Point sequence that is increasing or decreasing in height vs. point sequence that alternates in height

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	COMMENTS	`All examples in this Problem are groups of 3 dots.` `Any example where 2 adjacent dots have the same height would be ambiguously sorted.`
	CROSSREFS	`Adjacent-numbered pages: BP553 BP554 BP555 BP556 BP557 * BP559 BP560 BP561 BP562 BP563`
	EXAMPLE	`Reading from right to left in the first box on the left hand side: the 2nd dot is higher than the 1st, and the 3rd is higher than the 2nd, so the sequence of dots is strictly increasing in height.`
	KEYWORD	`nice, precise, antihuman, orderedtriplet, preciseworld`
	CONCEPT	`coordinate (info \| search)`
	WORLD	`three_points [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP559

Cross section of a cube vs. not cross section of a cube

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

	COMMENTS	`All examples are solid black shapes.` `This problem is absurdly hard. It makes a good extreme example. - Aaron David Fairbanks, Nov 23 2020`
	CROSSREFS	`Adjacent-numbered pages: BP554 BP555 BP556 BP557 BP558 * BP560 BP561 BP562 BP563 BP564`
	KEYWORD	`hard, precise, allsorted, notso, stretch, challenge, left-narrow, perfect`
	CONCEPT	`cube (info \| search),` `cross_section (info \| search)`
	WORLD	`fill_shape [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP560

There exists a closed trail that hits each edge exactly once vs. not so.

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

	COMMENTS	`Left examples are called "Eulerian graphs."` `A connected graph is Eulerian if and only if each vertex is incident to an even number of edges.`
	CROSSREFS	`Adjacent-numbered pages: BP555 BP556 BP557 BP558 BP559 * BP561 BP562 BP563 BP564 BP565`
	KEYWORD	`precise, allsorted, math, traditional, preciseworld`
	CONCEPT	`graph (info \| search),` `distinguishing_crossing_curves (info \| search),` `all (info \| search),` `even_odd (info \| search),` `existence (info \| search)`
	WORLD	`connected_graph [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP561

Meta Bongard Problems fitting in their own world vs. other meta Bongard Problems.

BP561

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

	COMMENTS	`This prompts thinking about left-self and right-self keywords.`
	CROSSREFS	`Adjacent-numbered pages: BP556 BP557 BP558 BP559 BP560 * BP562 BP563 BP564 BP565 BP566`
	KEYWORD	`stub, meta (see left/right), links, left-self, sideless, metameta`
	WORLD	`linksbp [smaller \| same \| bigger] zoom in left (bp_in_own_world)`
	AUTHOR	`Aaron David Fairbanks`

BP562

There exists a closed trail that hits each vertex exactly once vs. not so.

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

	COMMENTS	`Left examples are called "Hamiltonian graphs."`
	CROSSREFS	`Adjacent-numbered pages: BP557 BP558 BP559 BP560 BP561 * BP563 BP564 BP565 BP566 BP567`
	KEYWORD	`math, traditional`
	CONCEPT	`graph (info \| search),` `distinguishing_crossing_curves (info \| search)`
	WORLD	`connected_graph [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

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