The On-Line Encyclopedia of Bongard Problems

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Convex vs. concave.

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	COMMENTS	`All examples in this Problem are outlines of shapes or solid black shapes.`
	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 215.`
	CROSSREFS	`BP136 is the same solution (flipped) but with only polygonal outlines and also with extraneous dots distracting from the solution.` `Adjacent-numbered pages: BP1 BP2 BP3 * BP5 BP6 BP7 BP8 BP9`
	KEYWORD	`easy, nice, precise, unstable, right-narrow, finished, traditional, bongard`
	CONCEPT	`concave_convex_angle (info \| search)`
	WORLD	`outline_or_fill_shape [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

One line vs. two lines.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 224.`
	CROSSREFS	`Adjacent-numbered pages: BP26 BP27 BP28 BP29 BP30 * BP32 BP33 BP34 BP35 BP36`
	KEYWORD	`easy, precise, allsorted, left-narrow, right-narrow, pixelperfect, traditional, bongard`
	CONCEPT	`distinguishing_crossing_curves (info \| search),` `one (info \| search),` `two (info \| search)`
	WORLD	`smooth_crosscurves [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

All sides are equal vs. all angles are equal.

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	CROSSREFS	`Adjacent-numbered pages: BP323 BP324 BP325 BP326 BP327 * BP329 BP330 BP331 BP332 BP333`
	KEYWORD	`nice, stretch, left-narrow, right-narrow, traditional, finishedexamples, both`
	CONCEPT	`angle (info \| search),` `length_line_or_curve (info \| search),` `same_feature (info \| search),` `same (info \| search)`
	WORLD	`polygon_outline [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Odd number of dots vs. even number of dots.

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	CROSSREFS	`See BP334 for a version of the same idea, but using arbitrary shapes instead of dots.` `Adjacent-numbered pages: BP329 BP330 BP331 BP332 BP333 * BP335 BP336 BP337 BP338 BP339`
	KEYWORD	`precise, allsorted, number, math, left-narrow, right-narrow, right-null, help, traditional, preciseworld`
	CONCEPT	`even_odd (info \| search)`
	WORLD	`dots [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Intersection of circle and square vs. union of circle and square.

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	COMMENTS	`An image of only a circle or of only a square would be ambiguously categorized.`
	CROSSREFS	`Adjacent-numbered pages: BP340 BP341 BP342 BP343 BP344 * BP346 BP347 BP348 BP349 BP350`
	KEYWORD	`nice, left-narrow, right-narrow, traditional, both`
	CONCEPT	`set_intersection (info \| search),` `set_union (info \| search),` `imagined_shape (info \| search),` `imagined_entity (info \| search),` `overlap (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

No pattern (variety of shapes) vs. all shapes have something in common.

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	CROSSREFS	`See BP378 for a similar idea using just two objects per example.` `Adjacent-numbered pages: BP342 BP343 BP344 BP345 BP346 * BP348 BP349 BP350 BP351 BP352`
	KEYWORD	`nice, left-unknowable, right-narrow, traditional, collection`
	CONCEPT	`existence (info \| search),` `shape_cluster (info \| search),` `cluster_of_one (info \| search),` `cluster (info \| search)`
	WORLD	`several_small_misc [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Random arrangement of pixels vs. not so.

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	COMMENTS	`By "random" we mean it's reasonable to expect each pixel in the image was chosen with a constant, consistent chance of being black or white.`
	CROSSREFS	`Adjacent-numbered pages: BP354 BP355 BP356 BP357 BP358 * BP360 BP361 BP362 BP363 BP364`
	KEYWORD	`nice, right-narrow, collective, experimental, blackwhiteinvariant`
	CONCEPT	`pattern_or_random (info \| search)`
	WORLD	`bmp [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Intersection (logical conjunction) vs. union (logical disjunction).

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	CROSSREFS	`Adjacent-numbered pages: BP368 BP369 BP370 BP371 BP372 * BP374 BP375 BP376 BP377 BP378`
	KEYWORD	`abstract, anticomputer, concept, creativeexamples, left-narrow, right-narrow, contributepairs, traditional, miniworlds, dithering`
	CONCEPT	`set_intersection (info \| search),` `set_union (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

Image of a Bongard Problem with no simple solution versus image of a Bongard Problem with a simple solution.

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	COMMENTS	`Left examples have no solution, but they do not break the rules in ways so extreme that it is plainly impossible for them to have a solution, such as including the same image on both sides or including no images per side. (See such as including the same image on both sides or including no images per side.`
	CROSSREFS	`See BP522 for the version with links to pages on the OEBP instead of images of Bongard Problems (miniproblems).` `See BP968 (flipped) for a version of this Bongard Problem including examples of invalid Bongard Problems that don't even admit a convoluted solution (the same image appears on both sides).` `Also see BP1080, which is similar to BP968, but including various different formats of Bongard Problems, distinguishing them from arbitrary images that are not Bongard Problems.` `Adjacent-numbered pages: BP824 BP825 BP826 BP827 BP828 * BP830 BP831 BP832 BP833 BP834`
	KEYWORD	`nice, meta (see left/right), miniproblems, creativeexamples, left-unknowable, right-narrow, assumesfamiliarity, structure, help, presentationinvariant`
	CONCEPT	`existence (info \| search),` `simplicity (info \| search),` `zero (info \| search)`
	WORLD	`boxes_bpimage_three_per_side_nosoln_allowed [smaller \| same \| bigger] zoom in right (boxes_bpimage_three_per_side)`
	AUTHOR	`Aaron David Fairbanks`

Shape can be maneuvered around the corner vs. not so.

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	REFERENCE	`https://en.wikipedia.org/wiki/Moving_sofa_problem`
	CROSSREFS	`Adjacent-numbered pages: BP845 BP846 BP847 BP848 BP849 * BP851 BP852 BP853 BP854 BP855`
	KEYWORD	`nice, precise, physics, creativeexamples, proofsrequired, left-narrow, right-narrow, dithering`
	CONCEPT	`rotation_required (info \| search),` `imagined_motion (info \| search),` `physically_fitting (info \| search)`
	AUTHOR	`Leo Crabbe`

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