The On-Line Encyclopedia of Bongard Problems

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BP343

No two shapes are the same vs. at least two shapes are the same.

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	CROSSREFS	`BP57 is the same solution except all examples have two shapes.` `Adjacent-numbered pages: BP338 BP339 BP340 BP341 BP342 * BP344 BP345 BP346 BP347 BP348`
	KEYWORD	`traditional, collection`
	CONCEPT	`existence (info \| search),` `identical (info \| search),` `same_shape (info \| search),` `same (info \| search),` `two (info \| search)`
	WORLD	`shapes [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP347

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`

BP349

One object does not belong to the pattern of the rest vs. all objects form one pattern.

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	COMMENTS	`The left examples are the right examples with one object altered, which makes the solution easier to see.` `"Odd one out."`
	CROSSREFS	`Adjacent-numbered pages: BP344 BP345 BP346 BP347 BP348 * BP350 BP351 BP352 BP353 BP354`
	KEYWORD	`anticomputer, help, contributepairs, traditional, rules, collection`
	CONCEPT	`categorization (info \| search),` `existence (info \| search),` `feature_cluster (info \| search),` `number_cluster (info \| search),` `shape_cluster (info \| search),` `cluster_of_one (info \| search),` `cluster (info \| search),` `one (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP368

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`

BP391

There exists an edge such that removing it yields two disconnected graphs (i.e., the minimum number of edges whose removal results in two disconnected graphs is 1) vs. the minimum number of edges whose removal results in two disconnected graphs is 2.

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	CROSSREFS	`Adjacent-numbered pages: BP386 BP387 BP388 BP389 BP390 * BP392 BP393 BP394 BP395 BP396`
	KEYWORD	`nice, precise, traditional, preciseworld`
	CONCEPT	`graph (info \| search),` `distinguishing_crossing_curves (info \| search),` `existence (info \| search),` `imagined_shape (info \| search),` `imagined_entity (info \| search)`
	WORLD	`connected_graph [smaller \| same \| bigger]`
	AUTHOR	`Jago Collins`

BP394

For each colored square only, there exists a path starting on it that covers each square of the figure exactly once vs. there is no path that starts on a colored square and covers each square of the figure exactly once.

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	CROSSREFS	`Adjacent-numbered pages: BP389 BP390 BP391 BP392 BP393 * BP395 BP396 BP397 BP398 BP399`
	KEYWORD	`hard, nice, solved, traditional, dithering, left-listable, right-listable`
	CONCEPT	`existence (info \| search),` `path (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search)`
	AUTHOR	`Jago Collins`

BP544

Everything vs. nothing.

	&(%	0	BP1	BP544	BP1073
		dog	nothing

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	COMMENTS	`All ideas and things, with no limits.`
	CROSSREFS	`Adjacent-numbered pages: BP539 BP540 BP541 BP542 BP543 * BP545 BP546 BP547 BP548 BP549`
	KEYWORD	`notso, meta (see left/right), links, world, left-self, right-finite, right-full, left-null, left-it, feedback, experimental, funny`
	CONCEPT	`existence (info \| search)`
	WORLD	`everything [smaller \| same] zoom in left (everything) \| zoom in right (nothing)`
	AUTHOR	`Aaron David Fairbanks`

BP560

There exists a closed trail that hits each edge exactly once vs. not so.

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	COMMENTS	`Left examples are called "Eulerian graphs."` `A connected graph is Eulerian if and only if each vertex is incident to an even number of edges.`
	CROSSREFS	`Adjacent-numbered pages: BP555 BP556 BP557 BP558 BP559 * BP561 BP562 BP563 BP564 BP565`
	KEYWORD	`precise, allsorted, math, traditional, preciseworld`
	CONCEPT	`graph (info \| search),` `distinguishing_crossing_curves (info \| search),` `all (info \| search),` `even_odd (info \| search),` `existence (info \| search)`
	WORLD	`connected_graph [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP829

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`

BP832

Image of a Bongard Problem with solution presence of a specific object vs. image of a Bongard Problem with solution presence of a type of object.

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	COMMENTS	`"Specific object" we mean the same connected figure (up to movement around the box). It is ambiguous whether a scaled, rotated, or reflected version of an object would be considered "the same object" because no examples on either side are forced to deal with that subtlety in their respective solutions.`
	CROSSREFS	`Adjacent-numbered pages: BP827 BP828 BP829 BP830 BP831 * BP833 BP834 BP835 BP836 BP837`
	KEYWORD	`meta (see left/right), miniproblems, assumesfamiliarity, structure, presentationinvariant`
	CONCEPT	`existence (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

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