The On-Line Encyclopedia of Bongard Problems

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BP112

X-coordinates of dots are equidistant vs. y-coordinates of dots are equidistant.

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	CROSSREFS	`Adjacent-numbered pages: BP107 BP108 BP109 BP110 BP111 * BP113 BP114 BP115 BP116 BP117`
	KEYWORD	`hard, nice, antihuman, traditional`
	CONCEPT	`coordinate (info \| search),` `length_line_or_curve (info \| search),` `midpoint (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search),` `same_feature (info \| search),` `same (info \| search)`
	WORLD	`three_points [smaller \| same \| bigger]`
	AUTHOR	`Douglas R. Hofstadter`

BP162

Every other side, if extended, passes through one point vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP157 BP158 BP159 BP160 BP161 * BP163 BP164 BP165 BP166 BP167`
	KEYWORD	`hard, noisy, traditional`
	CONCEPT	`lines_coincide (info \| search),` `every_other (info \| search),` `imagined_point (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search)`
	AUTHOR	`Harry E. Foundalis`

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`

BP383

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`

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`

BP559

Cross section of a cube vs. not cross section of a cube

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	COMMENTS	`All examples are solid black shapes.` `This problem is absurdly hard. It makes a good extreme example. - Aaron David Fairbanks, Nov 23 2020`
	CROSSREFS	`Adjacent-numbered pages: BP554 BP555 BP556 BP557 BP558 * BP560 BP561 BP562 BP563 BP564`
	KEYWORD	`hard, precise, allsorted, notso, stretch, challenge, left-narrow, perfect`
	CONCEPT	`cube (info \| search),` `cross_section (info \| search)`
	WORLD	`fill_shape [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP564

Discrete points intersecting boundary of convex hull vs. connected segment intersecting boundary of convex hull

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	COMMENTS	`If a "string" is wound tightly around the shape, does one of its segments lie directly on the shape?` `All examples in this Problem are connected line segments or curves.` `We are taking lines here to be infinitely thin, so that if the boundary of the convex hull intersects the endpoint of a line exactly it is understood that they meet at 1 point.`
	CROSSREFS	`Adjacent-numbered pages: BP559 BP560 BP561 BP562 BP563 * BP565 BP566 BP567 BP568 BP569`
	EXAMPLE	`Imagine wrapping a string around the pointed star. This string would take the shape of the boundary of the star's convex hull (a regular pentagon), and would only touch the star at the end of each of its 5 individual tips, therefore the star belongs on the left.`
	KEYWORD	`hard, nice, allsorted, solved, perfect`
	AUTHOR	`Leo Crabbe`

BP793

Image of a Bongard Problem that would sort itself on its own left versus image of a Bongard Problem that would sort itself on its own right.

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	COMMENTS	`Rhetorical question: Where does this Bongard Problem sort an image of itself?` `See BP999 and BP1004 for similar paradoxes.` `Bongard Problems fitting left here evidently come in three categories: 1) would sort all Bongard Problems with the same solution left, 2) would sort all Bongard Problems with the same solution right, or 3) would sort some Bongard Problems with the same solution left and some right. See BP927.`
	CROSSREFS	`See BP517 for the version with links to pages on the OEBP instead of images of Bongard Problems (miniproblems).` `See BP954, which is about Bongard Problems not only sorting themselves, but moreover fractally appearing in themselves as panels.` `Adjacent-numbered pages: BP788 BP789 BP790 BP791 BP792 * BP794 BP795 BP796 BP797 BP798`
	KEYWORD	`hard, nice, abstract, dual, handed, leftright, solved, meta (see left/right), miniproblems, creativeexamples, presentationmatters, assumesfamiliarity, structure, experimental`
	WORLD	`boxes_bpimage_sorts_self [smaller \| same \| bigger] zoom in left (boxes_bpimage_sorts_self_left) \| zoom in right (boxes_bpimage_sorts_self_right)`
	AUTHOR	`Aaron David Fairbanks`

BP795

Image of a Bongard Problem that would sort itself on its own right versus image of a Bongard Problem that would sort itself on its own left.

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	COMMENTS	`"BONGARD HELL."` `This the flipped version of BP793 but using only images of Bongard Problems with solution "__ half more black/less white than other half versus vice versa," that all use rotated, reflected, and inverted versions of the same examples.`
	CROSSREFS	`See BP971 (left vs. right more black) and BP972 (top vs. bottom more black).` `Adjacent-numbered pages: BP790 BP791 BP792 BP793 BP794 * BP796 BP797 BP798 BP799 BP800`
	KEYWORD	`hard, nice, abstract, dual, handed, leftright, meta (see left/right), miniproblems, presentationmatters, left-finite, right-finite, assumesfamiliarity, structure, experimental, funny`
	WORLD	`bongard_hell [smaller \| same \| bigger] zoom in left \| zoom in right`
	AUTHOR	`Aaron David Fairbanks`

BP796

Image of a Bongard Problem that would sort a blank panel on its left versus image of a Bongard Problem that would sort a blank panel on its right.

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	CROSSREFS	`See BP567 for the version with links to pages on the OEBP instead of images of Bongard Problems (miniproblems).` `Adjacent-numbered pages: BP791 BP792 BP793 BP794 BP795 * BP797 BP798 BP799 BP800 BP801`
	KEYWORD	`hard, nice, abstract, dual, handed, leftright, challenge, meta (see left/right), miniproblems, creativeexamples, assumesfamiliarity, structure, presentationinvariant`
	WORLD	`boxes_bpimage [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

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