The On-Line Encyclopedia of Bongard Problems

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There exists a loop that passes through every white square once without passing through the black square vs. there exists no such loop.

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	CROSSREFS	`Adjacent-numbered pages: BP992 BP993 BP994 BP995 BP996 * BP998 BP999 BP1000 BP1001 BP1002`
	KEYWORD	`precise, allsorted, grid, preciseworld, left-listable, right-listable`
	CONCEPT	`path (info \| search)`
	AUTHOR	`James Tanton`

BP996

Net corresponds to a convex solid vs. net corresponds to a concave solid.

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	CROSSREFS	`Adjacent-numbered pages: BP991 BP992 BP993 BP994 BP995 * BP997 BP998 BP999 BP1000 BP1001`
	KEYWORD	`precise, 3d, perfect, preciseworld`
	WORLD	`polyhedron_net_unique_solid [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP994

Net corresponds to a solid that can tessellate 3D space vs. net does not correspond to a solid that can tessellate 3D space.

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	COMMENTS	`More specifically these solids are polyhedra, and are often called "space-filling".` `There is ambiguity here regarding some nets that can be folded to make multiple different solids. For example EX8175 could correspond to a cuboid with a pyramid-like protrusion at each end, a protrusion at one end and an indent at the other, or 2 indents. Only the second of these options can tessellate 3D space. For clarity's sake examples like this are not sorted on either side.`
	CROSSREFS	`Adjacent-numbered pages: BP989 BP990 BP991 BP992 BP993 * BP995 BP996 BP997 BP998 BP999`
	KEYWORD	`stub, precise, 3d, perfect, preciseworld`
	CONCEPT	`3d_net (info \| search),` `3d_solid (info \| search)`
	WORLD	`polyhedron_net [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP993

Net corresponds do a unique solid vs. net can be folded into multiple different solids.

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

	COMMENTS	`Right-sorted examples are called common nets.`
	CROSSREFS	`https://en.wikipedia.org/wiki/Common_net` `Adjacent-numbered pages: BP988 BP989 BP990 BP991 BP992 * BP994 BP995 BP996 BP997 BP998`
	KEYWORD	`stub, precise, 3d, perfect, preciseworld`
	CONCEPT	`rigidity (info \| search),` `3d_net (info \| search),` `3d_solid (info \| search),` `convey_enough_information (info \| search)`
	WORLD	`polyhedron_net [smaller \| same \| bigger] zoom in left (polyhedron_net_unique_solid)`
	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`

BP991

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

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	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`

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.

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	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`

BP989

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

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	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`

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`

BP986

Palindromes vs. not palindromes.

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	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`
	CONCEPT	`element_wise_symmetry (info \| search),` `identical (info \| search),` `sequence (info \| search),` `same_shape (info \| search),` `same (info \| search),` `symmetry (info \| search)`
	WORLD	`zoom in left \| zoom in right`
	AUTHOR	`Jago Collins`

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