The On-Line Encyclopedia of Bongard Problems

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There is a way of grouping elements into (more than one) equal-sized blocks such that no block appears twice vs. there exists no such grouping.

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	COMMENTS	`Sequences with a prime number of elements are sorted left when all their elements are unique, and sorted right otherwise.`
	CROSSREFS	`Adjacent-numbered pages: BP1270 BP1271 BP1272 BP1273 BP1274 * BP1276 BP1277 BP1278 BP1279 BP1280`
	EXAMPLE	`The sequence ABBABB would be sorted left, as it could be grouped into (AB)(BA)(BB), where each block is unique.`
	KEYWORD	`precise, unwordable, notso, sequence, miniworlds`
	CONCEPT	`element_grouping (info \| search)`
	AUTHOR	`Leo Crabbe`

BP202

Even number vs. odd number.

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

	CROSSREFS	`See BP334 for a version of the same idea, but using dots instead of arbitrary shapes.` `Adjacent-numbered pages: BP197 BP198 BP199 BP200 BP201 * BP203 BP204 BP205 BP206 BP207`
	KEYWORD	`noisy, number, traditional`
	CONCEPT	`even_odd (info \| search)`
	AUTHOR	`Giuseppe Insana`

BP809

Figures can be transformed into one another by smooth stretching (before and after there are the same crossroad-points; there is a curve connecting points before if and only if there is a curve connecting those points after) vs. not so.

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

	COMMENTS	`Left examples are topologically homeomorphic figures.` `For some examples one can imagine pulling the shape "out of" the 2d square in 3d in order to transform it, and then laying it flat back in the 2d square. See BP810 for the version where this is not allowed.`
	CROSSREFS	`Adjacent-numbered pages: BP804 BP805 BP806 BP807 BP808 * BP810 BP811 BP812 BP813 BP814`
	KEYWORD	`nice, math, unorderedpair, traditional`
	CONCEPT	`topological_transformation (info \| search)`
	WORLD	`two_figures_made_of_curves [smaller \| same \| bigger] zoom in left (two_homeomorphic_figures_made_of_curves)`
	AUTHOR	`Aaron David Fairbanks`

BP86

Three parts vs. five parts.

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

	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 242.`
	CROSSREFS	`Adjacent-numbered pages: BP81 BP82 BP83 BP84 BP85 * BP87 BP88 BP89 BP90 BP91`
	KEYWORD	`number, finished, traditional, bongard`
	CONCEPT	`branch_point (info \| search),` `lines_coincide (info \| search),` `number (info \| search),` `three (info \| search),` `five (info \| search)`
	AUTHOR	`Mikhail M. Bongard`

BP218

Something is missing vs. an extra copy of something is added.

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	COMMENTS	`A generalization of Hofstadter's BP148.`
	CROSSREFS	`Adjacent-numbered pages: BP213 BP214 BP215 BP216 BP217 * BP219 BP220 BP221 BP222 BP223`
	KEYWORD	`nice, abstract, traditional`
	CONCEPT	`missing_part (info \| search),` `regular_irregular_change (info \| search),` `extra_part (info \| search)`
	AUTHOR	`Giuseppe Insana`

BP1070

Dead end vs. no dead ends.

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	CROSSREFS	`Adjacent-numbered pages: BP1065 BP1066 BP1067 BP1068 BP1069 * BP1071 BP1072 BP1073 BP1074 BP1075`
	KEYWORD	`perfect, infinitedetail`
	CONCEPT	`finite_infinite (info \| search),` `fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search)`
	WORLD	`recursive_boxes [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP184

Curve is smooth close to the middle vs. curve zigzags close to the middle.

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

	CROSSREFS	`Adjacent-numbered pages: BP179 BP180 BP181 BP182 BP183 * BP185 BP186 BP187 BP188 BP189`
	KEYWORD	`traditional`
	CONCEPT	`imagined_point (info \| search),` `imagined_entity (info \| search),` `curve_texture (info \| search),` `texture (info \| search)`
	WORLD	`curve [smaller \| same \| bigger]`
	AUTHOR	`Harry E. Foundalis`

BP99

Outlines made by triangles and circles intersect vs. outlines made by triangles and circles do not intersect.

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

	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 246.`
	CROSSREFS	`Adjacent-numbered pages: BP94 BP95 BP96 BP97 BP98 * BP100 BP101 BP102 BP103 BP104`
	KEYWORD	`finished, traditional, bongard`
	CONCEPT	`collinear (info \| search),` `x-crossing (info \| search),` `cluster (info \| search)`
	AUTHOR	`Mikhail M. Bongard`

BP926

Numbers of dots in ascending order from left to right vs. numbers of dots neither in ascending nor descending order from left to right.

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

	CROSSREFS	`Adjacent-numbered pages: BP921 BP922 BP923 BP924 BP925 * BP927 BP928 BP929 BP930 BP931`
	KEYWORD	`nice, math, sequence, traditional, left-listable, right-listable`
	CONCEPT	`number (info \| search),` `dot (info \| search)`
	WORLD	`dot_clusters_sequence_horizontal [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP17

Shape with a reflex corner vs. shape without a reflex corner.

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

	COMMENTS	`All examples in this Bongard Problem are outlines of shapes.`
	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 219.`
	CROSSREFS	`Adjacent-numbered pages: BP12 BP13 BP14 BP15 BP16 * BP18 BP19 BP20 BP21 BP22`
	KEYWORD	`finished, traditional, bongard`
	CONCEPT	`acute (info \| search),` `angle (info \| search),` `indentation (info \| search)`
	WORLD	`shape_outline [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

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