The On-Line Encyclopedia of Bongard Problems

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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`

Two independent quantities changing simultaneously vs. determined by just one changing quantity.

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	COMMENTS	`Examples sorted right may feature multiple quantities, but one changing quantity determines all changing quantities.` `The distinction between the two sides is fuzzy. For example the left-sorted example EX4364 could be viewed as determined by just the one changing quantity of width and the fact that the height is given by two times the width minus one. On the other hand the right-sorted example EX4370 could be viewed as determined by the two changing quantities number of black squares and number of white squares, ignoring the fact that the total number of squares is always six.`
	CROSSREFS	`Adjacent-numbered pages: BP360 BP361 BP362 BP363 BP364 * BP366 BP367 BP368 BP369 BP370`
	KEYWORD	`fuzzy, traditional, rules, miniworlds`
	CONCEPT	`size_increase_decrease (info \| search),` `tracing_line_or_curve (info \| search)`
	WORLD	`constant_change_seq_increase_right [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Center of mass within the black area of the shape vs. center of mass out of the black area of the shape.

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	CROSSREFS	`Adjacent-numbered pages: BP362 BP363 BP364 BP365 BP366 * BP368 BP369 BP370 BP371 BP372`
	KEYWORD	`precise, unstable, physics, perfect, pixelperfect, traditional`
	CONCEPT	`inside (info \| search),` `center_of_mass (info \| search)`
	WORLD	`shape [smaller \| same \| bigger] zoom in left (shape_center_of_mass_falls_inside)`
	AUTHOR	`Aaron David Fairbanks`

There is a point that can see (in straight lines) all points vs. there is no point that can see (in straight lines) all points.

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	COMMENTS	`Left examples are called "star domains."`
	CROSSREFS	`See BP388 for whether a distinguished point can see all points.` `Adjacent-numbered pages: BP363 BP364 BP365 BP366 BP367 * BP369 BP370 BP371 BP372 BP373`
	KEYWORD	`nice, precise, unstable, perfect, traditional`
	CONCEPT	`all (info \| search),` `existence (info \| search),` `imagined_point (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search)`
	WORLD	`shape [smaller \| same \| bigger] zoom in left (fill_shape_with_seeing_point)`
	AUTHOR	`Aaron David Fairbanks`

Net (folding along edges can make a 3D solid) vs. not a net.

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	CROSSREFS	`Adjacent-numbered pages: BP366 BP367 BP368 BP369 BP370 * BP372 BP373 BP374 BP375 BP376`
	KEYWORD	`math`
	CONCEPT	`3d_net (info \| search),` `3d_solid (info \| search)`
	WORLD	`polygon_outlines_sharing_edges [smaller \| same \| bigger] zoom in left (polyhedron_net)`
	AUTHOR	`Aaron David Fairbanks`

Shape below fits on the left vs. shape below fits on the right.

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	COMMENTS	`See BP805 for the version of this with box-based BPs.`
	CROSSREFS	`Adjacent-numbered pages: BP367 BP368 BP369 BP370 BP371 * BP373 BP374 BP375 BP376 BP377`
	KEYWORD	`nice, dual, handed, leftright, creativeexamples, structure, traditional, rules`
	CONCEPT	`bongard_problem (info \| search),` `categorization (info \| search),` `feature_cluster (info \| search),` `cluster (info \| search),` `choice (info \| search)`
	WORLD	`bdimage_shapes_extra_below_clear_sort [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Complete finite collection vs. incomplete finite collection.

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	COMMENTS	`Related to BP380 and BP792.`
	CROSSREFS	`Adjacent-numbered pages: BP374 BP375 BP376 BP377 BP378 * BP380 BP381 BP382 BP383 BP384`
	KEYWORD	`nice, abstract, rules, miniworlds, collection`
	CONCEPT	`completeness (info \| search)`
	WORLD	`collection_of_objects_same_type [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

No knot (unknot) vs. knot.

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	COMMENTS	`To hint at the solution, left examples can be arranged in a sequence to show the unknot tying itself.`
	CROSSREFS	`Adjacent-numbered pages: BP377 BP378 BP379 BP380 BP381 * BP383 BP384 BP385 BP386 BP387`
	KEYWORD	`nice, math, anticomputer, help, traditional`
	CONCEPT	`knot (info \| search),` `topological_transformation (info \| search)`
	WORLD	`knot [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

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, collection`
	CONCEPT	`square_number (info \| search)`
	WORLD	`dots [smaller \| same \| bigger]`
	AUTHOR	`Jago Collins`

Nets of cubes vs. not nets of cubes.

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	CROSSREFS	`Adjacent-numbered pages: BP380 BP381 BP382 BP383 BP384 * BP386 BP387 BP388 BP389 BP390`
	KEYWORD	`nice, notso, left-finite, traditional`
	CONCEPT	`3d_net (info \| search)`
	WORLD	`square_outlines_sharing_edges [smaller \| same \| bigger] zoom in left (cube_net)`
	AUTHOR	`Jago Collins`

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