The On-Line Encyclopedia of Bongard Problems

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Bongard Problem with solution relating to concept: comparison of multiple quantities (within one example) vs. Bongard Problem unrelated to this concept.

BP7	BP27	BP28	BP29	BP36	BP37
BP38	BP53	BP969	BP970	BP1208	BP1214
BP1217

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	COMMENTS	`"More," "fewer," "greater than," "less than."` `See BP752 and BP749 for equality.`
	CROSSREFS	`Adjacent-numbered pages: BP978 BP979 BP980 BP981 BP982 * BP984 BP985 BP986 BP987 BP988`
	KEYWORD	`meta (see left/right), links, metaconcept`
	CONCEPT	`This MBP is about BPs that feature concept: "quantity_comparison"` `Searchable synonyms: "more", "less", "greater", "lesser", "greater than", "less than", "fewer".`
	WORLD	`bp [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP984

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

	BP35	BP39	BP72	BP73	BP101	BP165
	BP239	BP248	BP255

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

	CROSSREFS	`Adjacent-numbered pages: BP979 BP980 BP981 BP982 BP983 * BP985 BP986 BP987 BP988 BP989`
	KEYWORD	`meta (see left/right), links, metaconcept`
	CONCEPT	`This MBP is about BPs that feature concept: "parallel"`
	WORLD	`bp [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP985

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

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

	CROSSREFS	`Adjacent-numbered pages: BP980 BP981 BP982 BP983 BP984 * BP986 BP987 BP988 BP989 BP990`
	KEYWORD	`meta (see left/right), links, metaconcept`
	CONCEPT	`This MBP is about BPs that feature concept: "perpendicular"`
	WORLD	`bp [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP986

Palindromes vs. not palindromes.

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

	COMMENTS	`All examples in this Problem are sequences of graphic symbols. In this Problem, a "palindrome" is taken to be an ordered sequence which is the same read left-to-right as it is read right-to-left. A more formal solution to this Problem could be: "Sequences which are invariant under a permutation which swaps first and last entries, second and second last entries, third and third last entries, ... and so on vs. sequences which are not invariant under the aforementioned permutamation."`
	CROSSREFS	`Adjacent-numbered pages: BP981 BP982 BP983 BP984 BP985 * BP987 BP988 BP989 BP990 BP991`
	KEYWORD	`nice, precise, allsorted, notso, sequence, traditional, miniworlds`
	CONCEPT	`element_wise_symmetry (info \| search),` `identical (info \| search),` `sequence (info \| search),` `same_shape (info \| search),` `same (info \| search),` `symmetry (info \| search)`
	WORLD	`[smaller \| same \| bigger] zoom in left \| zoom in right`
	AUTHOR	`Jago Collins`

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.

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

	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`

BP988

Number of dots is a power of 2 vs. not so.

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	COMMENTS	`Numbers of dots on the left can be obtained by repeatedly doubling 1 dot.` `Numbers of dots on the left are the number of corners of a cube in some dimension.`
	CROSSREFS	`Adjacent-numbered pages: BP983 BP984 BP985 BP986 BP987 * BP989 BP990 BP991 BP992 BP993`
	KEYWORD	`stub, precise, allsorted, number, left-narrow, right-null, help, preciseworld`
	WORLD	`dots [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP989

Number of dots is n factorial for some n vs. not so.

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

	COMMENTS	`Zero is intentionally left out to avoid confusion (although it would fit right).`
	CROSSREFS	`Adjacent-numbered pages: BP984 BP985 BP986 BP987 BP988 * BP990 BP991 BP992 BP993 BP994`
	KEYWORD	`stub, precise, number, math, left-narrow, right-null, help, preciseworld`
	WORLD	`dots [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP990

The center of mass can "see" (in straight lines) all points within the shape vs. the center of mass is not located in a region where it can see (in straight lines) all points.

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

	COMMENTS	`Another way of thinking about the solution is considering whether a light source placed at the center of mass of a given example would illuminate the whole shape.`
	CROSSREFS	`Every left for this Problem would be will be a left example for both BP367 and BP368.` `Adjacent-numbered pages: BP985 BP986 BP987 BP988 BP989 * BP991 BP992 BP993 BP994 BP995`
	KEYWORD	`convoluted, perfect`
	CONCEPT	`inside (info \| search),` `center_of_mass (info \| search),` `imagined_point (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search)`
	WORLD	`fill_shape_seeing_point_center_of_mass_inside [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP991

Can be arranged with multiple copies of itself to form some convex shape vs. not so.

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

	CROSSREFS	`This is a generalization of BP820.` `Adjacent-numbered pages: BP986 BP987 BP988 BP989 BP990 * BP992 BP993 BP994 BP995 BP996`
	KEYWORD	`precise, allsorted, perfect`
	CONCEPT	`tiling (info \| search)`
	WORLD	`fill_shape [smaller \| same \| bigger] zoom in left`
	AUTHOR	`Leo Crabbe`

BP992

Concave shapes with concave cavities vs. convex cavities

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	COMMENTS	`All examples in this Problem are solid concave black shapes. In this Problem, the "cavities" of a concave shape are defined to be the convex hull of the shape minus the shape itself. For example, if you take a bite out of the edge of a piece of paper, the piece of paper in your mouth is the cavity of the bitten piece of paper. The idea may be indefinitely extended, considering whether the cavities of the cavities are concave or convex, and so on.`
	CROSSREFS	`Adjacent-numbered pages: BP987 BP988 BP989 BP990 BP991 * BP993 BP994 BP995 BP996 BP997`
	KEYWORD	`nice, precise, perfect, traditional`
	CONCEPT	`recursion_number (info \| search),` `recursion (info \| search)`
	WORLD	`concave_fill_shape [smaller \| same \| bigger]`
	AUTHOR	`Jago Collins`

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