The On-Line Encyclopedia of Bongard Problems

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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`

BP354

Increasing quantity is angular vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP349 BP350 BP351 BP352 BP353 * BP355 BP356 BP357 BP358 BP359`
	KEYWORD	`creativeexamples, structure, sequence, traditional, rules, miniworlds`
	CONCEPT	`angle (info \| search),` `loop (info \| search),` `tracing_line_or_curve (info \| search)`
	WORLD	`constant_change_seq_increase_right [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP869

Approximately symmetric vs. asymmetric.

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

	COMMENTS	`Or, "evokes idea of symmetry (see BP760) vs. not so," which is also a solution for BP847. - Aaron David Fairbanks, Jul 29 2020`
	CROSSREFS	`Adjacent-numbered pages: BP864 BP865 BP866 BP867 BP868 * BP870 BP871 BP872 BP873 BP874`
	KEYWORD	`abstract, spectrum, anticomputer, subjective, concept, perfect`
	CONCEPT	`imperfection_small (info \| search),` `symmetry (info \| search)`
	AUTHOR	`Leo Crabbe`

BP1157

The order in which the objects in the top half are combined to make the object in the lower half matters vs. not so.

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	COMMENTS	`Operations depicted in right-sorted examples are called "commutative".` `"Order matters" here means that if the objects in the top half were to switch places, the output would look different.`
	REFERENCE	`https://en.wikipedia.org/wiki/Commutative_property`
	CROSSREFS	`Adjacent-numbered pages: BP1152 BP1153 BP1154 BP1155 BP1156 * BP1158 BP1159 BP1160 BP1161 BP1162`
	KEYWORD	`nice, abstract, unwordable, notso, structure, rules, miniworlds`
	CONCEPT	`function (info \| search)`
	AUTHOR	`Leo Crabbe`

BP331

Image of something 2-D vs. image of something 3-D.

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

	CROSSREFS	`Adjacent-numbered pages: BP326 BP327 BP328 BP329 BP330 * BP332 BP333 BP334 BP335 BP336`
	KEYWORD	`abstract, anticomputer, collective, traditional, dithering`
	CONCEPT	`dimensionality (info \| search),` `3d_solid (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP183

Same curvature close to the middle vs. change of curvature close to the middle.

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	CROSSREFS	`Adjacent-numbered pages: BP178 BP179 BP180 BP181 BP182 * BP184 BP185 BP186 BP187 BP188`
	KEYWORD	`noisy, traditional`
	CONCEPT	`sides_of_line (info \| search),` `tangent (info \| search),` `imagined_point (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search)`
	WORLD	`curve [smaller \| same \| bigger]`
	AUTHOR	`Harry E. Foundalis`

BP132

Dots are vertices of a triangle standing on a side vs. dots are vertices of a triangle standing on a vertex.

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

	CROSSREFS	`Adjacent-numbered pages: BP127 BP128 BP129 BP130 BP131 * BP133 BP134 BP135 BP136 BP137`
	KEYWORD	`noisy, traditional`
	CONCEPT	`base (info \| search),` `horizontal (info \| search),` `vertex_of_meeting_lines (info \| search),` `triangle (info \| search),` `vertical (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

BP990

The center of mass can "see" (in straight lines) all points within the shape vs. the center of mass is not located in a region where it can see (in straight lines) all points.

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	COMMENTS	`Another way of thinking about the solution is considering whether a light source placed at the center of mass of a given example would illuminate the whole shape.`
	CROSSREFS	`Every left for this Problem would be will be a left example for both BP367 and BP368.` `Adjacent-numbered pages: BP985 BP986 BP987 BP988 BP989 * BP991 BP992 BP993 BP994 BP995`
	KEYWORD	`convoluted, perfect`
	CONCEPT	`inside (info \| search),` `center_of_mass (info \| search),` `imagined_point (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search)`
	WORLD	`fill_shape_seeing_point_center_of_mass_inside [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP1282

If two players take turns moving moving the black circles with the intention of capturing their opponent's piece, one can always "checkmate" the other vs. the game results in a draw if the players play optimally.

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	COMMENTS	`Players can only move their piece to a node connected to their current position. A win is secured by moving to a node your opponent is occupying.` `Which player that can force a win in left-sorted examples can change depending on who moves first.`
	CROSSREFS	`See BP1284 for an animated Problem about the same game.` `Adjacent-numbered pages: BP1277 BP1278 BP1279 BP1280 BP1281 * BP1283 BP1284 BP1285 BP1286 BP1287`
	KEYWORD	`allsorted, unwordable, notso, teach`
	CONCEPT	`capture_game (info \| search)`
	AUTHOR	`Leo Crabbe`

BP334

Odd number of dots vs. even number of dots.

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	CROSSREFS	`See BP334 for a version of the same idea, but using arbitrary shapes instead of dots.` `Adjacent-numbered pages: BP329 BP330 BP331 BP332 BP333 * BP335 BP336 BP337 BP338 BP339`
	KEYWORD	`precise, allsorted, number, math, left-narrow, right-narrow, right-null, help, traditional, preciseworld`
	CONCEPT	`even_odd (info \| search)`
	WORLD	`dots [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

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