The On-Line Encyclopedia of Bongard Problems

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BP131

Dots are vertices of a parallelogram vs. dots are not vertices of a parallelogram.

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	CROSSREFS	`Adjacent-numbered pages: BP126 BP127 BP128 BP129 BP130 * BP132 BP133 BP134 BP135 BP136`
	KEYWORD	`noisy, traditional`
	CONCEPT	`existence (info \| search),` `length_line_or_curve (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

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`

BP259

Two identical overlapping objects of which the top is rotated slightly clockwise vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP254 BP255 BP256 BP257 BP258 * BP260 BP261 BP262 BP263 BP264`
	KEYWORD	`traditional`
	CONCEPT	`turn_orientation (info \| search),` `rotation_required (info \| search),` `objects_overlap (info \| search),` `overlap (info \| search),` `same_shape (info \| search),` `same (info \| search)`
	AUTHOR	`Andreas Gunnarsson`

BP126

One large and one small object vs. not so.

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

	CROSSREFS	`Adjacent-numbered pages: BP121 BP122 BP123 BP124 BP125 * BP127 BP128 BP129 BP130 BP131`
	KEYWORD	`traditional`
	CONCEPT	`number (info \| search),` `separation_of_joined_objects (info \| search),` `size (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

BP1063

Specific structure vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP1058 BP1059 BP1060 BP1061 BP1062 * BP1064 BP1065 BP1066 BP1067 BP1068`
	KEYWORD	`notso, arbitrary, perfect, infinitedetail`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search),` `specificity (info \| search),` `one (info \| search),` `two (info \| search),` `three (info \| search)`
	WORLD	`recursive_boxes [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1131

One shape can be totally obscured by the other vs. neither shape can be obscured.

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	COMMENTS	`Rotation of shapes is not required for any left-hand panels, but it should not change any example's sorting if it is considered.`
	CROSSREFS	`Adjacent-numbered pages: BP1126 BP1127 BP1128 BP1129 BP1130 * BP1132 BP1133 BP1134 BP1135 BP1136`
	KEYWORD	`nice, precise, allsorted, pixelperfect, unorderedpair`
	CONCEPT	`overlap (info \| search)`
	WORLD	`2_shapes [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP141

Two clusters of three and two objects each vs. one cluster of three objects and two different objects.

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

	CROSSREFS	`Adjacent-numbered pages: BP136 BP137 BP138 BP139 BP140 * BP142 BP143 BP144 BP145 BP146`
	KEYWORD	`traditional`
	CONCEPT	`and (info \| search),` `number (info \| search),` `feature_cluster (info \| search),` `cluster (info \| search),` `same_shape (info \| search),` `same (info \| search),` `one (info \| search),` `two (info \| search),` `three (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

BP997

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`

BP230

The sum of vertices, line ends, and dots is 7 vs. not so.

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

	CROSSREFS	`Adjacent-numbered pages: BP225 BP226 BP227 BP228 BP229 * BP231 BP232 BP233 BP234 BP235`
	KEYWORD	`arbitrary, traditional`
	CONCEPT	`addition (info \| search),` `line_or_curve_endpoint (info \| search),` `dot (info \| search),` `vertex_of_meeting_lines (info \| search)`
	AUTHOR	`Giuseppe Insana`

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`

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