The On-Line Encyclopedia of Bongard Problems

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BP1

Empty image vs. non-empty image.

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	COMMENTS	`The first Bongard Problem.` `All examples in this Bongard Problem are line drawings (one or more connected figures made up of curved and non-curved lines).`
	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 214.`
	CROSSREFS	`Adjacent-numbered pages: * BP2 BP3 BP4 BP5 BP6`
	EXAMPLE	`A circle fits on the right because it is not nothing.`
	KEYWORD	`easy, nice, precise, allsorted, unstable, world, left-narrow, left-finite, left-full, left-null, perfect, pixelperfect, finished, traditional, stableworld, deformstable, bongard`
	CONCEPT	`empty (info \| search),` `existence (info \| search),` `zero (info \| search)`
	WORLD	`zoom in left (blank_image) \| zoom in right (curves_drawing)`
	AUTHOR	`Mikhail M. Bongard`

BP31

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`

BP50

Vertical axis of symmetry vs. no axis of symmetry.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 230.`
	CROSSREFS	`BP152 is the same solution (with the sides switched), using connected shapes and without black filling.` `BP1206 was created to be a slightly different version of this: "vertical axis of symmetry vs. no vertical axis of symmetry." (That less specific solution fits this Bongard Problem as well.)` `Adjacent-numbered pages: BP45 BP46 BP47 BP48 BP49 * BP51 BP52 BP53 BP54 BP55`
	KEYWORD	`nice, stretch, left-narrow, finished, traditional, bongard`
	CONCEPT	`symmetry_axis (info \| search),` `symmetry (info \| search)`
	WORLD	`curves_and_fill_shapes_separate_drawing [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

BP328

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`

BP334

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`

BP345

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`

BP356

Object at lower-right fits as n-th item in the top row of objects, where n is the number of dots at lower-left vs. not so.

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	COMMENTS	`All examples have a number of dots in the bottom left corner, an object in the bottom right corner, and a sequence of object at the top.`
	CROSSREFS	`Adjacent-numbered pages: BP351 BP352 BP353 BP354 BP355 * BP357 BP358 BP359 BP360 BP361`
	KEYWORD	`nice, creativeexamples, left-narrow, structure, traditional, rules, miniworlds`
	CONCEPT	`fractal (info \| search),` `iteration (info \| search),` `tracing_line_or_curve (info \| search),` `feature_cluster (info \| search),` `shape_cluster (info \| search),` `cluster (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP373

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`

BP384

Square number of dots vs. non-square number of dots.

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	COMMENTS	`All examples in this Problem are a collection of dots.` `An equivalent solution is "Dots can be arranged into a square lattice whose convex hull is a square vs. not so". - Leo Crabbe, Aug 01 2020`
	CROSSREFS	`Adjacent-numbered pages: BP379 BP380 BP381 BP382 BP383 * BP385 BP386 BP387 BP388 BP389`
	EXAMPLE	`A single dot fits because 1 = 11.` `A pair of dots does not fit because there is no integer x such that 2 = xx.`
	KEYWORD	`nice, precise, allsorted, number, math, left-narrow, left-null, help, traditional, preciseworld`
	CONCEPT	`square_number (info \| search)`
	WORLD	`dots [smaller \| same \| bigger]`
	AUTHOR	`Jago Collins`

BP386

Lower shape can be used as a tile to build the upper one vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP381 BP382 BP383 BP384 BP385 * BP387 BP388 BP389 BP390 BP391`
	KEYWORD	`nice, precise, allsorted, left-narrow, perfect, pixelperfect, orderedpair, traditional, preciseworld, left-listable, right-listable`
	CONCEPT	`tiling (info \| search)`
	AUTHOR	`Jago Collins`

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