The On-Line Encyclopedia of Bongard Problems

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BP242

Convex hull is a square vs. convex hull is not a square.

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

	COMMENTS	`Additionally, the points in the examples on the left lie on the boundary of the square.` `EX2897 was originally on the right hand side, but it was removed because it seems to be an error.`
	CROSSREFS	`Adjacent-numbered pages: BP237 BP238 BP239 BP240 BP241 * BP243 BP244 BP245 BP246 BP247`
	KEYWORD	`noisy, traditional`
	CONCEPT	`convex_hull (info \| search),` `square (info \| search)`
	AUTHOR	`Matthew J. Howells`

BP1051

White is multiple of black vs. not so.

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

	CROSSREFS	`Adjacent-numbered pages: BP1046 BP1047 BP1048 BP1049 BP1050 * BP1052 BP1053 BP1054 BP1055 BP1056`
	KEYWORD	`precise, allsorted, preciseworld`
	CONCEPT	`ratio (info \| search)`
	WORLD	`outline_or_fill_circles_same_size [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP142

Two clusters of three and two that are adjacent vs. two clusters of three and two that are not adjacent.

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

	CROSSREFS	`Adjacent-numbered pages: BP137 BP138 BP139 BP140 BP141 * BP143 BP144 BP145 BP146 BP147`
	KEYWORD	`traditional, miniworlds`
	CONCEPT	`adjacent (info \| search),` `and (info \| search),` `feature_cluster (info \| search),` `cluster (info \| search),` `same_shape (info \| search),` `same (info \| search),` `two (info \| search),` `three (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

BP19

Horizontal pinch vs. vertical pinch.

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

	COMMENTS	`All examples in this Bongard Problem are outlines of shapes. More specifically, all examples have a thin horizontal or vertical bridge in the middle connecting two wide ends.`
	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 220.`
	CROSSREFS	`Adjacent-numbered pages: BP14 BP15 BP16 BP17 BP18 * BP20 BP21 BP22 BP23 BP24`
	KEYWORD	`dual, rotate, finished, traditional, bongard`
	CONCEPT	`horizontal (info \| search),` `neck_narrowing (info \| search),` `vertical (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

BP816

Cross section of a cylinder vs. not cross section of a cylinder

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

	CROSSREFS	`Adjacent-numbered pages: BP811 BP812 BP813 BP814 BP815 * BP817 BP818 BP819 BP820 BP821`
	KEYWORD	`precise, notso, stretch, unstable, perfect`
	CONCEPT	`cross_section (info \| search)`
	WORLD	`fill_shapes [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP263

At least one ending edge is straight vs. all ending edges are curved.

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

	CROSSREFS	`Adjacent-numbered pages: BP258 BP259 BP260 BP261 BP262 * BP264 BP265 BP266 BP267 BP268`
	KEYWORD	`traditional`
	CONCEPT	`curved_straight (info \| search),` `slope_at_endpoint (info \| search)`
	AUTHOR	`Pablo Barenbaum`

BP892

Black shapes can be arranged such that they fit inside rectangular outline vs. not so.

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

	COMMENTS	`There is a slight ambiguity here regarding whether a shape could be placed within another shape's hole. This is a question of how one perceives the Problem: are we sliding shapes around on a table in 2D or are we allowed to 'lift' them in 3D space?`
	CROSSREFS	`Adjacent-numbered pages: BP887 BP888 BP889 BP890 BP891 * BP893 BP894 BP895 BP896 BP897`
	KEYWORD	`nice, precise, perfect, pixelperfect, help`
	CONCEPT	`rotation_required (info \| search),` `physically_fitting (info \| search)`
	AUTHOR	`Leo Crabbe`

BP376

A "chess piece" that moves as shown may reach every square vs. not so.

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

	CROSSREFS	`Adjacent-numbered pages: BP371 BP372 BP373 BP374 BP375 * BP377 BP378 BP379 BP380 BP381`
	KEYWORD	`precise, allsorted, notso, left-finite, right-finite, fixedgrid, preciseworld`
	CONCEPT	`all (info \| search),` `chess-like (info \| search),` `imagined_motion (info \| search),` `motion (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP248

Dashed lines inside solid shape make an identical but slightly smaller shape, parallel to the one outside vs. not so.

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

	CROSSREFS	`Adjacent-numbered pages: BP243 BP244 BP245 BP246 BP247 * BP249 BP250 BP251 BP252 BP253`
	KEYWORD	`traditional`
	CONCEPT	`inside (info \| search),` `size (info \| search),` `similar_shape (info \| search),` `similar (info \| search),` `curve_texture (info \| search),` `texture (info \| search),` `parallel (info \| search)`
	AUTHOR	`Andreas Gunnarsson`

BP948

Image of Bongard Problem such that pixel-inverting examples flips the solution vs. image of Bongard Problem such that pixel-inverting examples leaves the solution invariant.

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

	CROSSREFS	`See BP556 (keyword blackwhite) for the version with links to pages on the OEBP instead of images of Bongard Problems.` `Adjacent-numbered pages: BP943 BP944 BP945 BP946 BP947 * BP949 BP950 BP951 BP952 BP953`
	KEYWORD	`meta (see left/right), miniproblems, presentationinvariant`
	CONCEPT	`black_white_inversion (info \| search)`
	AUTHOR	`Leo Crabbe`

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