The On-Line Encyclopedia of Bongard Problems

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Empty image vs. non-empty image.

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	COMMENTS	`The first Bongard Problem.` `All examples in this Bongard Problem are line drawings (one or more connected figures made up of curved and non-curved lines).`
	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 214.`
	CROSSREFS	`Adjacent-numbered pages: * BP2 BP3 BP4 BP5 BP6`
	EXAMPLE	`A circle fits on the right because it is not nothing.`
	KEYWORD	`easy, nice, precise, allsorted, unstable, world, left-narrow, left-finite, left-full, left-null, perfect, pixelperfect, finished, traditional, stableworld, deformstable, bongard`
	CONCEPT	`empty (info \| search),` `existence (info \| search),` `zero (info \| search)`
	WORLD	`zoom in left (blank_image) \| zoom in right (curves_drawing)`
	AUTHOR	`Mikhail M. Bongard`

Quadrilateral that is nearly a triangle vs. typical quadrilateral.

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	CROSSREFS	`Adjacent-numbered pages: BP155 BP156 BP157 BP158 BP159 * BP161 BP162 BP163 BP164 BP165`
	KEYWORD	`perfect, traditional`
	CONCEPT	`imperfection_small (info \| search),` `number (info \| search),` `triangle (info \| search)`
	WORLD	`Multiple options: [smaller \| same \| bigger], quadrilateral_outline [smaller \| same \| bigger]`
	AUTHOR	`Harry E. Foundalis`

Stays put vs. tumbles.

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	CROSSREFS	`BP273 has the same solution, except all examples are letters.` `Adjacent-numbered pages: BP194 BP195 BP196 BP197 BP198 * BP200 BP201 BP202 BP203 BP204`
	KEYWORD	`nice, handed, updown, rotate, physics, anticomputer, perfect`
	CONCEPT	`base (info \| search),` `downward_upward (info \| search),` `tumbles_or_stays_put (info \| search),` `line_absolute_direction (info \| search),` `absolute_direction (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search),` `direction (info \| search),` `gravity (info \| search)`
	AUTHOR	`Harry E. Foundalis`

Part of at least one object is out of box vs. all objects are within the box.

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	COMMENTS	`Alternatively, "black touches the boundary vs. not".`
	CROSSREFS	`Adjacent-numbered pages: BP205 BP206 BP207 BP208 BP209 * BP211 BP212 BP213 BP214 BP215`
	KEYWORD	`precise, boundingbox, perfect, pixelperfect, traditional, bordercontent`
	CONCEPT	`completed_out_of_box (info \| search),` `existence (info \| search)`
	AUTHOR	`Giuseppe Insana`

More black than white vs. more white than black.

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	CROSSREFS	`See BP196 for a version of this Problem restricted to uniform textures.` `Adjacent-numbered pages: BP206 BP207 BP208 BP209 BP210 * BP212 BP213 BP214 BP215 BP216`
	KEYWORD	`easy, nice, spectrum, dual, blackwhite, unstable, right-null, perfect, pixelperfect, traditional, continuous, viceversa, bordercontent`
	CONCEPT	`outlined_filled (info \| search),` `size (info \| search),` `texture (info \| search)`
	WORLD	`bmp [smaller \| same \| bigger] zoom in left \| zoom in right`
	AUTHOR	`Giuseppe Insana`

The tightest-curved section, out of all sections of curve that make a complete turn (360 degrees), contains an x-crossing point vs. not so.

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	COMMENTS	`All examples are connected smooth curves allowed to self-intersect that must curve in only one direction (starting at one end, either clockwise or counter-clockwise), i.e. there is no inflection point.`
	CROSSREFS	`Adjacent-numbered pages: BP208 BP209 BP210 BP211 BP212 * BP214 BP215 BP216 BP217 BP218`
	KEYWORD	`less, convoluted, perfect, traditional`
	CONCEPT	`x-crossing (info \| search)`
	AUTHOR	`Giuseppe Insana`

Ink tip (non-homogeneous line) vs. Marker tip (homogeneous line).

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	CROSSREFS	`Adjacent-numbered pages: BP211 BP212 BP213 BP214 BP215 * BP217 BP218 BP219 BP220 BP221`
	KEYWORD	`perfect`
	CONCEPT	`line_or_curve_endpoint (info \| search),` `curve_texture (info \| search),` `texture (info \| search)`
	AUTHOR	`Giuseppe Insana`

Totally black lines vs. lines with white specks.

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	CROSSREFS	`Adjacent-numbered pages: BP212 BP213 BP214 BP215 BP216 * BP218 BP219 BP220 BP221 BP222`
	KEYWORD	`perfect, pixelperfect`
	CONCEPT	`curve_texture (info \| search),` `texture (info \| search)`
	AUTHOR	`Giuseppe Insana`

Large black region if completed is a circle vs. large black region if completed is an ellipse.

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	CROSSREFS	`Adjacent-numbered pages: BP218 BP219 BP220 BP221 BP222 * BP224 BP225 BP226 BP227 BP228`
	KEYWORD	`noisy, perfect, traditional`
	CONCEPT	`imperfection_small (info \| search)`
	AUTHOR	`Giuseppe Insana`

Lines intersect within the box vs. lines intersect out of the box.

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	CROSSREFS	`Adjacent-numbered pages: BP307 BP308 BP309 BP310 BP311 * BP313 BP314 BP315 BP316 BP317`
	KEYWORD	`precise, allsorted, boundingbox, perfect, unorderedpair, traditional, preciseworld, absoluteposition`
	CONCEPT	`completed_out_of_box (info \| search),` `vertex_of_meeting_lines (info \| search),` `imagined_point (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search)`
	AUTHOR	`Jakub Štepo`

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