The On-Line Encyclopedia of Bongard Problems

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White dot can see (in straight lines) all black points vs. white dot cannot see (in straight lines) all black points.

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	CROSSREFS	`See BP368 for whether ALL points can see all points.` `Adjacent-numbered pages: BP383 BP384 BP385 BP386 BP387 * BP389 BP390 BP391 BP392 BP393`
	KEYWORD	`nice, traditional`
	CONCEPT	`all (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search)`
	WORLD	`fill_shape_white_dot [smaller \| same \| bigger]`
	AUTHOR	`Jago Collins`

Dots can be shared equally between figures vs. dots cannot be shared equally between figures.

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	CROSSREFS	`Adjacent-numbered pages: BP382 BP383 BP384 BP385 BP386 * BP388 BP389 BP390 BP391 BP392`
	KEYWORD	`nice, traditional`
	CONCEPT	`division (info \| search)`
	AUTHOR	`Jago Collins`

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`

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`

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`

When the shape is removed from the dots, the dots give enough information to place the shape back where it was vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP378 BP379 BP380 BP381 BP382 * BP384 BP385 BP386 BP387 BP388`
	KEYWORD	`hard, nice, traditional`
	CONCEPT	`imagined_line_or_curve (info \| search),` `imagined_entity (info \| search),` `convey_enough_information (info \| search)`
	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`

Adding the top two waves yields the bottom wave vs. not so.

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	COMMENTS	`This problem is about wave interference.`
	CROSSREFS	`Adjacent-numbered pages: BP376 BP377 BP378 BP379 BP380 * BP382 BP383 BP384 BP385 BP386`
	KEYWORD	`nice, notso, math, orderedtriplet, traditional`
	CONCEPT	`addition (info \| search),` `wave (info \| search),` `2_inputs_1_output (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

The completed version of the collection is finite vs. the completed version of the collection is infinite.

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	COMMENTS	`Related to BP379 and BP792.` `An example with clusters of perfect numbers of dots would be sorted ambiguously, for the time being. Unfortunately the 3rd smallest perfect number is 496. - Leo Crabbe, Oct 18 2024`
	CROSSREFS	`See also BP870.` `Adjacent-numbered pages: BP375 BP376 BP377 BP378 BP379 * BP381 BP382 BP383 BP384 BP385`
	KEYWORD	`math, creativeexamples, traditional, rules, miniworlds, collection`
	CONCEPT	`finite_infinite (info \| search)`
	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`

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