The On-Line Encyclopedia of Bongard Problems

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BP96

Triangles vs. quadrangles.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 245.`
	CROSSREFS	`Adjacent-numbered pages: BP91 BP92 BP93 BP94 BP95 * BP97 BP98 BP99 BP100 BP101`
	KEYWORD	`number, finished, traditional, bongard`
	CONCEPT	`collinear (info \| search),` `line_or_curve_endpoint (info \| search),` `number (info \| search),` `imagined_shape (info \| search),` `imagined_entity (info \| search)`
	AUTHOR	`Mikhail M. Bongard`

BP97

Triangles vs. circles.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 246.`
	CROSSREFS	`Adjacent-numbered pages: BP92 BP93 BP94 BP95 BP96 * BP98 BP99 BP100 BP101 BP102`
	KEYWORD	`easy, nice, finished, traditional, bongard`
	CONCEPT	`convex_hull (info \| search),` `imagined_shape (info \| search),` `imagined_entity (info \| search)`
	AUTHOR	`Mikhail M. Bongard`

BP101

Parallel dents vs. perpendicular dents.

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	CROSSREFS	`Adjacent-numbered pages: BP96 BP97 BP98 BP99 BP100 * BP102 BP103 BP104 BP105 BP106`
	KEYWORD	`traditional`
	CONCEPT	`indentation (info \| search),` `imagined_shape (info \| search),` `imagined_entity (info \| search),` `parallel (info \| search),` `perpendicular (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

BP138

No dot well within the convex hull vs. at least one dot well within the convex hull.

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	CROSSREFS	`Adjacent-numbered pages: BP133 BP134 BP135 BP136 BP137 * BP139 BP140 BP141 BP142 BP143`
	KEYWORD	`traditional`
	CONCEPT	`convex_hull (info \| search),` `existence (info \| search),` `imagined_shape (info \| search),` `imagined_entity (info \| search)`
	WORLD	`5_dots [smaller \| same \| bigger]`
	AUTHOR	`Douglas R. Hofstadter`

BP193

Ghost triangle vs. Ghost rectangle.

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	CROSSREFS	`Adjacent-numbered pages: BP188 BP189 BP190 BP191 BP192 * BP194 BP195 BP196 BP197 BP198`
	KEYWORD	`nice, anticomputer, traditional, dithering`
	CONCEPT	`absence_as_presence (info \| search),` `completed_out_of_box (info \| search),` `ghost (info \| search),` `number (info \| search),` `imagined_shape (info \| search),` `imagined_entity (info \| search),` `triangle (info \| search)`
	AUTHOR	`Harry E. Foundalis`

BP194

Background is a parallelogram vs. background is a triangle.

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	CROSSREFS	`Adjacent-numbered pages: BP189 BP190 BP191 BP192 BP193 * BP195 BP196 BP197 BP198 BP199`
	KEYWORD	`easy, nice, noisy, traditional`
	CONCEPT	`shape_background (info \| search),` `number (info \| search),` `imagined_shape (info \| search),` `imagined_entity (info \| search),` `triangle (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, nice, 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.

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	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`

BP362

Choice that solves the analogy exists vs. choice that solves the analogy does not exist.

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	CROSSREFS	`Adjacent-numbered pages: BP357 BP358 BP359 BP360 BP361 * BP363 BP364 BP365 BP366 BP367`
	KEYWORD	`creativeexamples, assumesfamiliarity, structure, rules`
	CONCEPT	`analogy (info \| search),` `imagined_shape (info \| search),` `imagined_entity (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP390

Each graph vertex is uniquely defined by its connections (the graph does not admit nontrivial automorphisms) vs. the graph admits nontrivial automorphisms.

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	CROSSREFS	`Adjacent-numbered pages: BP385 BP386 BP387 BP388 BP389 * BP391 BP392 BP393 BP394 BP395`
	KEYWORD	`precise, allsorted, notso, traditional, preciseworld`
	CONCEPT	`graph (info \| search),` `self-reference (info \| search),` `topological_transformation (info \| search),` `imagined_shape (info \| search),` `imagined_entity (info \| search)`
	WORLD	`connected_graph [smaller \| same \| bigger]`
	AUTHOR	`Jago Collins`

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