The On-Line Encyclopedia of Bongard Problems

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A circle is inside of a figure made by crosses vs. a circle is outside of figures made by crosses.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 241.`
	CROSSREFS	`Adjacent-numbered pages: BP78 BP79 BP80 BP81 BP82 * BP84 BP85 BP86 BP87 BP88`
	KEYWORD	`finished, traditional, bongard`
	CONCEPT	`convex_hull (info \| search),` `inside (info \| search),` `cluster_of_one (info \| search),` `cluster (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

The sum of all dot clumps has the same numerical property as each of the dot clumps vs. not so.

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	CROSSREFS	`This is a version of BP1003 with only numbers.` `Contrast BP1005, which is very similar.` `Adjacent-numbered pages: BP1001 BP1002 BP1003 BP1004 BP1005 * BP1007 BP1008 BP1009 BP1010 BP1011`
	KEYWORD	`nice, hardsort, left-narrow, rules`
	CONCEPT	`recursion (info \| search),` `self-reference (info \| search)`
	WORLD	`[smaller \| same \| bigger] zoom in left \| zoom in right`
	AUTHOR	`Leo Crabbe, Aaron David Fairbanks`

Exactly one point where lines bend at an angle vs. not exactly one point where lines bend at an angle.

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	CROSSREFS	`Adjacent-numbered pages: BP257 BP258 BP259 BP260 BP261 * BP263 BP264 BP265 BP266 BP267`
	KEYWORD	`less, convoluted, traditional`
	CONCEPT	`angle (info \| search),` `number (info \| search)`
	AUTHOR	`Pablo Barenbaum`

Lines if slightly extended make up a regular polygon vs. lines if slightly extended cannot make up a regular polygon.

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	CROSSREFS	`Adjacent-numbered pages: BP294 BP295 BP296 BP297 BP298 * BP300 BP301 BP302 BP303 BP304`
	KEYWORD	`traditional`
	CONCEPT	`imperfection_small (info \| search)`
	WORLD	`segments [smaller \| same \| bigger]`
	AUTHOR	`"Lewis"`

Reversible transformations vs. non-reversible transformations.

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	COMMENTS	`All examples depict a process that transforms one object into another (two example input-output pairs are provided in every panel). In left-sorted examples, each input corresponds to a unique output, whereas in right-sorted examples, different inputs could potentially lead to the same output. There is a sense in which all the processes described on the right "lose" some amount of the input's information.`
	REFERENCE	`https://en.wikipedia.org/wiki/Injective_function`
	CROSSREFS	`Adjacent-numbered pages: BP912 BP913 BP914 BP915 BP916 * BP918 BP919 BP920 BP921 BP922`
	KEYWORD	`nice, abstract, creativeexamples, structure, rules, miniworlds`
	CONCEPT	`convey_enough_information (info \| search),` `function (info \| search)`
	AUTHOR	`Leo Crabbe`

Circle centers are collinear vs. circle centers are not collinear.

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	CROSSREFS	`Adjacent-numbered pages: BP129 BP130 BP131 BP132 BP133 * BP135 BP136 BP137 BP138 BP139`
	KEYWORD	`traditional`
	CONCEPT	`all (info \| search),` `collinear (info \| search),` `center_of_circle (info \| search),` `center (info \| search),` `imagined_point (info \| search),` `imagined_entity (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

Neighbouring tiles share exactly 1 side vs not so.

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	CROSSREFS	`Adjacent-numbered pages: BP1008 BP1009 BP1010 BP1011 BP1012 * BP1014 BP1015 BP1016 BP1017 BP1018`
	KEYWORD	`precise, allsorted, perfect`
	CONCEPT	`infinite_plane (info \| search),` `tessellation (info \| search),` `tiling (info \| search)`
	WORLD	`wallpaper_tiling_1_polygon [smaller \| same \| bigger] zoom in left`
	AUTHOR	`Leo Crabbe`

Line perpendicular to one side of the object vs. line parallel to one side of the object.

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	CROSSREFS	`Adjacent-numbered pages: BP160 BP161 BP162 BP163 BP164 * BP166 BP167 BP168 BP169 BP170`
	KEYWORD	`noisy, orderedpair, traditional`
	CONCEPT	`parallel (info \| search),` `perpendicular (info \| search)`
	AUTHOR	`Harry E. Foundalis`

Filled subsection is largest square that divides the grid vs. not so

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	REFERENCE	`https://en.wikipedia.org/wiki/Greatest_common_divisor`
	CROSSREFS	`Any example in this BP is a left example of BP1057.` `Adjacent-numbered pages: BP1067 BP1068 BP1069 BP1070 BP1071 * BP1073 BP1074 BP1075 BP1076 BP1077`
	KEYWORD	`grid, left-listable, right-listable`
	CONCEPT	`division (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Jago Collins`

Bottom shape is bigger than top shape vs. top shape is bigger than bottom shape.

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	CROSSREFS	`BP1214 has the same solution but rotated a quarter-turn clockwise.` `Adjacent-numbered pages: BP1212 BP1213 BP1214 BP1215 BP1216 * BP1218 BP1219 BP1220 BP1221 BP1222`
	KEYWORD	`stub, dual, handed, updown, traditional`
	CONCEPT	`size (info \| search),` `quantity_comparison (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

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