The On-Line Encyclopedia of Bongard Problems

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BP45

Outline figure on top of solid black figure vs. black figure on top of outline figure.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 228.`
	CROSSREFS	`Adjacent-numbered pages: BP40 BP41 BP42 BP43 BP44 * BP46 BP47 BP48 BP49 BP50`
	KEYWORD	`dual, finished, traditional, viceversa, bongard`
	CONCEPT	`3d_front_back (info \| search),` `outlined_filled (info \| search),` `objects_overlap (info \| search),` `overlap (info \| search),` `texture (info \| search)`
	AUTHOR	`Mikhail M. Bongard`

BP46

Triangle on top of the circle vs. circle on top of the triangle.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 229.`
	CROSSREFS	`Adjacent-numbered pages: BP41 BP42 BP43 BP44 BP45 * BP47 BP48 BP49 BP50 BP51`
	KEYWORD	`finished, traditional, viceversa, bongard`
	CONCEPT	`3d_front_back (info \| search),` `objects_overlap (info \| search),` `overlap (info \| search),` `triangle (info \| search)`
	AUTHOR	`Mikhail M. Bongard`

BP81

Dark figures can be divided from outline figures by a straight line vs. convex hulls of filled and outlined figures overlap.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 240.`
	CROSSREFS	`Adjacent-numbered pages: BP76 BP77 BP78 BP79 BP80 * BP82 BP83 BP84 BP85 BP86`
	KEYWORD	`finished, traditional, bongard`
	CONCEPT	`convex_hull (info \| search),` `separable_entangled (info \| search),` `sides_of_line (info \| search),` `feature_cluster (info \| search),` `cluster_of_one (info \| search),` `cluster (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search),` `objects_overlap (info \| search),` `overlap (info \| search)`
	AUTHOR	`Mikhail M. Bongard`

BP163

Line connecting small shapes does not intersect large one vs. line connecting small shapes intersects large one.

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	CROSSREFS	`See BP1015 for a re-skinned version with dots instead of shapes.` `Adjacent-numbered pages: BP158 BP159 BP160 BP161 BP162 * BP164 BP165 BP166 BP167 BP168`
	KEYWORD	`traditional`
	CONCEPT	`imagined_line_or_curve (info \| search),` `imagined_entity (info \| search),` `object_line_overlap (info \| search),` `overlap (info \| search)`
	AUTHOR	`Harry E. Foundalis`

BP259

Two identical overlapping objects of which the top is rotated slightly clockwise vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP254 BP255 BP256 BP257 BP258 * BP260 BP261 BP262 BP263 BP264`
	KEYWORD	`traditional`
	CONCEPT	`turn_orientation (info \| search),` `rotation_required (info \| search),` `objects_overlap (info \| search),` `overlap (info \| search),` `same_shape (info \| search),` `same (info \| search)`
	AUTHOR	`Andreas Gunnarsson`

BP275

Straight line joining the ends does not intersect the object vs. straight line joining the ends intersects the object.

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	CROSSREFS	`Adjacent-numbered pages: BP270 BP271 BP272 BP273 BP274 * BP276 BP277 BP278 BP279 BP280`
	CONCEPT	`imagined_line_or_curve (info \| search),` `imagined_entity (info \| search),` `object_line_overlap (info \| search),` `overlap (info \| search)`
	WORLD	`arial_font_centered_connected_symbol [smaller \| same \| bigger]`
	AUTHOR	`Merse E. Gáspár`

BP301

Large and medium-sized square, the latter can be hidden vs. large and small-sized square, the latter can be hidden.

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	CROSSREFS	`Adjacent-numbered pages: BP296 BP297 BP298 BP299 BP300 * BP302 BP303 BP304 BP305 BP306`
	KEYWORD	`invalid, traditional`
	CONCEPT	`outlined_filled (info \| search),` `size (info \| search),` `objects_overlap (info \| search),` `overlap (info \| search),` `texture (info \| search)`
	AUTHOR	`"Lewis"`

BP325

Left shapes can combine by symmetric difference (XOR logical operator) to make right shape vs. left shapes can combine by intersection (AND logical operator) to make right shape.

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	CROSSREFS	`Adjacent-numbered pages: BP320 BP321 BP322 BP323 BP324 * BP326 BP327 BP328 BP329 BP330`
	KEYWORD	`precise, unstable, perfect, pixelperfect, structure, orderedtriplet, traditional`
	CONCEPT	`xor (info \| search),` `overlap (info \| search)`
	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`

BP1015

Segment drawn between two points intersects another line vs segment drawn between two points does not intersect any other lines

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	CROSSREFS	`This is nearly identical to BP163. Here instead of shape outlines dots are used, and the dots can be within the larger shape outline.` `Adjacent-numbered pages: BP1010 BP1011 BP1012 BP1013 BP1014 * BP1016 BP1017 BP1018 BP1019 BP1020`
	KEYWORD	`easy, precise`
	CONCEPT	`dot (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search),` `object_line_overlap (info \| search),` `overlap (info \| search)`
	AUTHOR	`Peter Nesin`

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