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`

BP344

Shape can tile itself vs. shape cannot tile itself.

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	COMMENTS	`Left examples are sometimes called "rep-tiles."` `The tiles all must be the same size. More specifically, all left examples can tile themselves only using scaled down and rotated versions of themselves with all tiles the same size. Right examples cannot tile themselves using scaled down rotated versions of themselves or even reflected versions of themselves with all tiles the same size.` `Without the puzzle piece-like shape EX4120 on the right side the current examples also allow the solution "shape can tile with itself so as to create a parallelogram vs. shape cannot tile with itself so as to create a parallelogram."`
	CROSSREFS	`See BP532 for a version with fractals.` `Adjacent-numbered pages: BP339 BP340 BP341 BP342 BP343 * BP345 BP346 BP347 BP348 BP349`
	EXAMPLE	`Go to https://oebp.org/files/yet.png for an illustration of how some left-sorted shapes tile themselves.`
	KEYWORD	`hard, precise, notso, unstable, math, hardsort, creativeexamples, proofsrequired, perfect, traditional`
	CONCEPT	`recursion (info \| search),` `self-reference (info \| search),` `tiling (info \| search),` `imagined_shape (info \| search),` `imagined_entity (info \| search)`
	WORLD	`shape [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP345

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

(edit; present; nest [left/right]; search; history)

	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`

BP346

Object on the right fits in pattern on the left vs. object on the right does not fit in pattern on the left.

(edit; present; nest [left/right]; search; history)

	CROSSREFS	`Adjacent-numbered pages: BP341 BP342 BP343 BP344 BP345 * BP347 BP348 BP349 BP350 BP351`
	KEYWORD	`nice, creativeexamples, structure, traditional, rules`
	CONCEPT	`categorization (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP347

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

(edit; present; nest [left/right]; search; history)

	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`

BP348

Shape on the right is the convex hull of shape on the left vs. not so.

(edit; present; nest [left/right]; search; history)

	CROSSREFS	`Adjacent-numbered pages: BP343 BP344 BP345 BP346 BP347 * BP349 BP350 BP351 BP352 BP353`
	KEYWORD	`precise, unstable, perfect, orderedpair, traditional`
	CONCEPT	`convex_hull (info \| search)`
	WORLD	`2_fill_shapes [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`

BP350

Some quantity keeps increasing from left to right vs. not so.

(edit; present; nest [left/right]; search; history)

	CROSSREFS	`Adjacent-numbered pages: BP345 BP346 BP347 BP348 BP349 * BP351 BP352 BP353 BP354 BP355`
	KEYWORD	`creativeexamples, structure, sequence, traditional, rules`
	CONCEPT	`size_increase_decrease (info \| search),` `iteration (info \| search),` `tracing_line_or_curve (info \| search)`
	WORLD	`quantity_vary_seq_noise_allowed [smaller \| same \| bigger] zoom in left (quantity_change_seq_increase_right_noise_allowed)`
	AUTHOR	`Aaron David Fairbanks`

BP351

Discrete quantity vs. continuous quantity.

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	CROSSREFS	`See BP873 for the version with Bongard Problems.` `Adjacent-numbered pages: BP346 BP347 BP348 BP349 BP350 * BP352 BP353 BP354 BP355 BP356`
	KEYWORD	`creativeexamples, structure, sequence, traditional, rules`
	CONCEPT	`size_increase_decrease (info \| search),` `discrete_continuous (info \| search),` `iteration (info \| search),` `tracing_line_or_curve (info \| search)`
	WORLD	`constant_change_seq_increase_right [smaller \| same \| bigger] zoom in left (constant_change_discrete_seq_increase_right)`
	AUTHOR	`Aaron David Fairbanks`

BP352

Increasing quantity has no lower (or upper) bound (and gives a representation of negative numbers) vs. increasing quantity has lower (and/or upper) bound.

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	COMMENTS	`All left examples have a clear "zero" value, but it may be unclear which side is meant to be positive and which side is meant to be negative (See BP893^left for quantities without clear notion of increase/decrease.)`
	CROSSREFS	`See BP353^left for looping quantities; these do not clearly represent positive and negative numbers, but they can likewise unboundedly decrease and increase.` `Adjacent-numbered pages: BP347 BP348 BP349 BP350 BP351 * BP353 BP354 BP355 BP356 BP357`
	KEYWORD	`creativeexamples, structure, sequence, traditional, rules`
	CONCEPT	`size_increase_decrease (info \| search),` `iteration (info \| search),` `tracing_line_or_curve (info \| search)`
	WORLD	`constant_change_seq_increase_right [smaller \| same \| bigger] zoom in right (constant_change_seq_increase_right_lower_bound)`
	AUTHOR	`Aaron David Fairbanks`

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