The On-Line Encyclopedia of Bongard Problems

Search: author:Douglas R. Hofstadter

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Concave shape vs. convex shape.

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	CROSSREFS	`BP4 is the same solution (flipped) but without the distracting dots (and also with some shapes filled in black and/or curvy instead of just polygon outlines).` `Adjacent-numbered pages: BP131 BP132 BP133 BP134 BP135 * BP137 BP138 BP139 BP140 BP141`
	KEYWORD	`noisy, ignoreimperfections, traditional`
	CONCEPT	`concave_convex_angle (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

Circles on same side of curve vs. circles on different sides of curves.

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	CROSSREFS	`Adjacent-numbered pages: BP130 BP131 BP132 BP133 BP134 * BP136 BP137 BP138 BP139 BP140`
	KEYWORD	`noisy, traditional`
	CONCEPT	`on_sides_of_curve (info \| search),` `separation_of_joined_objects (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

Circle centers are collinear vs. circle centers are not collinear.

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	CROSSREFS	`Adjacent-numbered pages: BP129 BP130 BP131 BP132 BP133 * BP135 BP136 BP137 BP138 BP139`
	KEYWORD	`traditional`
	CONCEPT	`all (info \| search),` `collinear (info \| search),` `center_of_circle (info \| search),` `center (info \| search),` `imagined_point (info \| search),` `imagined_entity (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

Dots collinear with center of circle vs. dots not collinear with center of circle.

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	CROSSREFS	`Adjacent-numbered pages: BP128 BP129 BP130 BP131 BP132 * BP134 BP135 BP136 BP137 BP138`
	KEYWORD	`traditional`
	CONCEPT	`all (info \| search),` `collinear (info \| search),` `center_of_circle (info \| search),` `center (info \| search),` `imagined_point (info \| search),` `imagined_entity (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

Dots are vertices of a triangle standing on a side vs. dots are vertices of a triangle standing on a vertex.

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	CROSSREFS	`Adjacent-numbered pages: BP127 BP128 BP129 BP130 BP131 * BP133 BP134 BP135 BP136 BP137`
	KEYWORD	`noisy, traditional`
	CONCEPT	`base (info \| search),` `horizontal (info \| search),` `vertex_of_meeting_lines (info \| search),` `triangle (info \| search),` `vertical (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

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`

Closed region is made of curves if flaws are ignored vs. closed region is a polygon if flaws are ignored.

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	CROSSREFS	`Adjacent-numbered pages: BP125 BP126 BP127 BP128 BP129 * BP131 BP132 BP133 BP134 BP135`
	KEYWORD	`noisy, traditional`
	CONCEPT	`curved_straight (info \| search),` `imperfection_small (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

Indentation on protrusion vs. indentation on indentation.

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	CROSSREFS	`Adjacent-numbered pages: BP124 BP125 BP126 BP127 BP128 * BP130 BP131 BP132 BP133 BP134`
	KEYWORD	`traditional`
	CONCEPT	`indentation (info \| search),` `protrusion (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

Same objects inside and outside the large shape vs. not same objects inside and outside the large shape.

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	CROSSREFS	`Adjacent-numbered pages: BP123 BP124 BP125 BP126 BP127 * BP129 BP130 BP131 BP132 BP133`
	KEYWORD	`noisy, traditional`
	CONCEPT	`inside (info \| search),` `interior_exterior (info \| search),` `outlined_filled (info \| search),` `shape_cluster (info \| search),` `cluster (info \| search),` `same_number (info \| search),` `same (info \| search),` `texture (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

Exactly one circle vs. not exactly one circle.

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	CROSSREFS	`Adjacent-numbered pages: BP122 BP123 BP124 BP125 BP126 * BP128 BP129 BP130 BP131 BP132`
	KEYWORD	`noisy, notso, traditional`
	CONCEPT	`exists_one (info \| search),` `number (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

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