The On-Line Encyclopedia of Bongard Problems

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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`

BP993

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

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	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`

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`

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`

BP1008

The 26th from the left, 63rd from the top pixel is black versus white.

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	COMMENTS	`This is a typical kind of joke answer people give for Bongard Problems when they cannot find an answer.`
	CROSSREFS	`Adjacent-numbered pages: BP1003 BP1004 BP1005 BP1006 BP1007 * BP1009 BP1010 BP1011 BP1012 BP1013`
	KEYWORD	`less, dual, arbitrary, handed, leftright, updown, boundingbox, blackwhite, antihuman, right-null, perfect, pixelperfect, help, experimental, funny, absoluteposition, bordercontent`
	CONCEPT	`specificity (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP1011

Polygon can be inscribed in a circle vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP1006 BP1007 BP1008 BP1009 BP1010 * BP1012 BP1013 BP1014 BP1015 BP1016`
	KEYWORD	`hard, precise, stretch, challenge, left-narrow, perfect, preciseworld`
	CONCEPT	`circle (info \| search),` `imagined_entity (info \| search)`
	WORLD	`fill_polygon [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP1012

No tile shares a partial side with another tile vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP1007 BP1008 BP1009 BP1010 BP1011 * BP1013 BP1014 BP1015 BP1016 BP1017`
	KEYWORD	`precise, allsorted, perfect`
	CONCEPT	`infinite_plane (info \| search),` `tessellation (info \| search),` `tiling (info \| search)`
	WORLD	`wallpaper_tiling_1_polygon [smaller \| same \| bigger] zoom in left`
	AUTHOR	`Leo Crabbe`

BP1013

Neighbouring tiles share exactly 1 side vs not so.

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	CROSSREFS	`Adjacent-numbered pages: BP1008 BP1009 BP1010 BP1011 BP1012 * BP1014 BP1015 BP1016 BP1017 BP1018`
	KEYWORD	`precise, allsorted, perfect`
	CONCEPT	`infinite_plane (info \| search),` `tessellation (info \| search),` `tiling (info \| search)`
	WORLD	`wallpaper_tiling_1_polygon [smaller \| same \| bigger] zoom in left`
	AUTHOR	`Leo Crabbe`

BP1017

Line segments linking same-coloured dots would intersect vs. not so.

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	CROSSREFS	`This is a less noisy version of BP261.` `Adjacent-numbered pages: BP1012 BP1013 BP1014 BP1015 BP1016 * BP1018 BP1019 BP1020 BP1021 BP1022`
	KEYWORD	`easy, nice, precise, allsorted, perfect, traditional, finishedexamples, preciseworld`
	CONCEPT	`lines_coincide (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search),` `overlap (info \| search)`
	AUTHOR	`Leo Crabbe`

BP1058

Top layer is two vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP1053 BP1054 BP1055 BP1056 BP1057 * BP1059 BP1060 BP1061 BP1062 BP1063`
	KEYWORD	`arbitrary, perfect, infinitedetail`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search),` `specificity (info \| search),` `two (info \| search)`
	WORLD	`recursive_boxes [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

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