The On-Line Encyclopedia of Bongard Problems

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Solid dark figures above the outline figures vs. outline figures above the solid dark figures.

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

	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 229.`
	CROSSREFS	`Adjacent-numbered pages: BP43 BP44 BP45 BP46 BP47 * BP49 BP50 BP51 BP52 BP53`
	KEYWORD	`noisy, finished, traditional, viceversa, bongard`
	CONCEPT	`above_below (info \| search),` `average (info \| search),` `outlined_filled (info \| search),` `feature_cluster (info \| search),` `cluster (info \| search),` `texture (info \| search)`
	WORLD	`circle_square_eq-tri_small_some_outline_some_fill [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

Three parts vs. four parts.

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

	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 243.`
	CROSSREFS	`Adjacent-numbered pages: BP85 BP86 BP87 BP88 BP89 * BP91 BP92 BP93 BP94 BP95`
	KEYWORD	`number, finished, traditional, bongard`
	CONCEPT	`number (info \| search),` `outlined_filled (info \| search),` `separation_of_joined_objects (info \| search),` `feature_cluster (info \| search),` `cluster_of_one (info \| search),` `cluster (info \| search),` `texture (info \| search),` `three (info \| search),` `four (info \| search)`
	AUTHOR	`Mikhail M. Bongard`

Objects below match their "symbols" above, according to one "code" versus objects below match their "symbols" above, according to another "code."

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

	COMMENTS	`Circle: VV; square: VΛ; triangle: ΛΛ ; blank: ΛV vs. circle: ΛΛ; square: ΛV; triangle: VV; blank: VΛ.`
	CROSSREFS	`Adjacent-numbered pages: BP116 BP117 BP118 BP119 BP120 * BP122 BP123 BP124 BP125 BP126`
	KEYWORD	`arbitrary, consistentsymbols, traditional`
	CONCEPT	`absence_as_presence (info \| search),` `correspondence (info \| search),` `sides_of_line (info \| search),` `triangle (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

Lone square vs. lone circle.

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

	CROSSREFS	`Adjacent-numbered pages: BP144 BP145 BP146 BP147 BP148 * BP150 BP151 BP152 BP153 BP154`
	KEYWORD	`traditional`
	CONCEPT	`near_far (info \| search),` `feature_cluster (info \| search),` `cluster_of_one (info \| search),` `cluster (info \| search),` `one (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

All clusters are made of objects of the same texture vs. not all clusters are made of objects of the same texture.

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	CROSSREFS	`Adjacent-numbered pages: BP184 BP185 BP186 BP187 BP188 * BP190 BP191 BP192 BP193 BP194`
	KEYWORD	`traditional`
	CONCEPT	`all (info \| search),` `outlined_filled (info \| search),` `feature_cluster (info \| search),` `cluster (info \| search),` `same_feature (info \| search),` `same (info \| search),` `texture (info \| search)`
	AUTHOR	`Harry E. Foundalis`

The shapes in the large square never appear outside of it vs. at least one shape in the large square appears outside of it.

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

	CROSSREFS	`Adjacent-numbered pages: BP286 BP287 BP288 BP289 BP290 * BP292 BP293 BP294 BP295 BP296`
	KEYWORD	`traditional`
	CONCEPT	`inside (info \| search),` `interior_exterior (info \| search)`
	AUTHOR	`"Lewis"`

Any transformation (rotation or flip) that sends one L to another L sends each L to some other L versus not so.

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	COMMENTS	`Restriction of BP841 to these axis-aligned L-shapes.` `Left examples represent subgroups of the dihedral group D4.`
	CROSSREFS	`Adjacent-numbered pages: BP835 BP836 BP837 BP838 BP839 * BP841 BP842 BP843 BP844 BP845`
	KEYWORD	`traditional`
	WORLD	`zoom in left \| zoom in right`
	AUTHOR	`Aaron David Fairbanks`

Nested pairs of brackets vs. other arrangement of brackets (some open brackets are not closed or there are extra closing brackets).

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	COMMENTS	`Examples on the left are also known as "Dyck words".`
	REFERENCE	`https://en.wikipedia.org/wiki/Dyck_language`
	CROSSREFS	`Adjacent-numbered pages: BP951 BP952 BP953 BP954 BP955 * BP957 BP958 BP959 BP960 BP961`
	KEYWORD	`easy, nice, precise, allsorted, unwordable, notso, sequence, traditional, inductivedefinition, preciseworld, left-listable, right-listable`
	CONCEPT	`recursion (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

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