The On-Line Encyclopedia of Bongard Problems

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BP146

A shape contains a square if and only if it is a circle vs. a shape contains a square if and only if it is a triangle.

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

	CROSSREFS	`Adjacent-numbered pages: BP141 BP142 BP143 BP144 BP145 * BP147 BP148 BP149 BP150 BP151`
	KEYWORD	`traditional`
	CONCEPT	`iff (info \| search),` `inside (info \| search),` `triangle (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

BP904

Rows show all possible ways a certain number of dots can be divided between a certain number of bins vs. not so.

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

	COMMENTS	`The rows in the panels on the right hand side show all the ways you can divide a certain number of dots between a certain number of bins, ignoring which bins they are placed in.`
	CROSSREFS	`Adjacent-numbered pages: BP899 BP900 BP901 BP902 BP903 * BP905 BP906 BP907 BP908 BP909`
	KEYWORD	`solved, left-null, grid, left-listable, right-listable`
	CONCEPT	`permutation (info \| search)`
	AUTHOR	`Molly C Klenzak`

BP13

Tall rectangle OR wide ellipse vs. wide rectangle OR tall ellipse.

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

	COMMENTS	`All examples in this Bongard Problem are outlines of ellipses or rectangles aligned to the x-y-axes.`
	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 218.`
	CROSSREFS	`Adjacent-numbered pages: BP8 BP9 BP10 BP11 BP12 * BP14 BP15 BP16 BP17 BP18`
	KEYWORD	`precise, stretch, finished, traditional, preciseworld, bongard`
	CONCEPT	`or (info \| search),` `horizontal (info \| search),` `line_slope (info \| search),` `vertical (info \| search)`
	WORLD	`rectangle_or_ellipse_outline_axis_aligned [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

BP375

Representationally uniform vs. representationally non-uniform.

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

	CROSSREFS	`Adjacent-numbered pages: BP370 BP371 BP372 BP373 BP374 * BP376 BP377 BP378 BP379 BP380`
	KEYWORD	`nice, traditional`
	CONCEPT	`simplicity (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP310

Enclosed square repelled by the outside squares, closest to the side of the enclosing square thats farthest from the common center of the outside squares. vs. enclosed square attracted by the outside squares, closest to the side of the enclosing square thats closest to the common center of the outside squares..

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

	CROSSREFS	`Adjacent-numbered pages: BP305 BP306 BP307 BP308 BP309 * BP311 BP312 BP313 BP314 BP315`
	KEYWORD	`traditional`
	CONCEPT	`cluster_barycenter (info \| search),` `inside (info \| search),` `interior_exterior (info \| search),` `near_far (info \| search),` `shape_cluster (info \| search),` `cluster (info \| search),` `imagined_point (info \| search),` `imagined_entity (info \| search)`
	AUTHOR	`"Lewis"`

BP339

Union of left sets is right set vs. intersection of left sets is right set.

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

	CROSSREFS	`Adjacent-numbered pages: BP334 BP335 BP336 BP337 BP338 * BP340 BP341 BP342 BP343 BP344`
	KEYWORD	`math, structure, orderedtriplet, traditional, both, neither`
	CONCEPT	`set_intersection (info \| search),` `left_right (info \| search),` `set_union (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP966

Even number of white regions vs. odd number of white regions.

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

	COMMENTS	`See BP889 for the version in which the background doesn't count.`
	CROSSREFS	`Adjacent-numbered pages: BP961 BP962 BP963 BP964 BP965 * BP967 BP968 BP969 BP970 BP971`
	KEYWORD	`nice, boundingbox, number, right-null, perfect, pixelperfect, traditional, bordercontent`
	CONCEPT	`separated_regions (info \| search),` `even_odd (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP1187

Smaller section tiles the grid vs. not so.

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

	CROSSREFS	`See BP1185 for the version of this solution where element-wise rotation of tiles is allowed.` `Adjacent-numbered pages: BP1182 BP1183 BP1184 BP1185 BP1186 * BP1188 BP1189 BP1190 BP1191 BP1192`
	KEYWORD	`allsorted, notso, grid`
	CONCEPT	`element_wise_symmetry (info \| search),` `tiling (info \| search)`
	AUTHOR	`Leo Crabbe`

BP805

Bongard Problem sorts example below on the left versus Bongard Problem sorts example below on the right.

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

	COMMENTS	`See BP372 for the version of this with BPs with black shapes as examples instead of boxes.`
	CROSSREFS	`Adjacent-numbered pages: BP800 BP801 BP802 BP803 BP804 * BP806 BP807 BP808 BP809 BP810`
	KEYWORD	`nice, dual, handed, leftright, creativeexamples, structure, contributepairs, rules`
	CONCEPT	`bongard_problem (info \| search),` `categorization (info \| search),` `choice (info \| search)`
	WORLD	`boxes_bdimage_six_per_side_extra_below_clear_sort [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP18

"Pinched" shape (drastically thinner somewhere in the middle than on the ends) vs. non-pinched shape.

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

	COMMENTS	`All examples in this Bongard Problem are oblong outlines of shapes.`
	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 219.`
	CROSSREFS	`Adjacent-numbered pages: BP13 BP14 BP15 BP16 BP17 * BP19 BP20 BP21 BP22 BP23`
	KEYWORD	`finished, traditional, bongard`
	CONCEPT	`neck_narrowing (info \| search)`
	WORLD	`elongated_outline [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

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