The On-Line Encyclopedia of Bongard Problems

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

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

	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`

All connected objects have the same texture vs. some connected objects have different textures.

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

	CROSSREFS	`Adjacent-numbered pages: BP185 BP186 BP187 BP188 BP189 * BP191 BP192 BP193 BP194 BP195`
	KEYWORD	`anticomputer, traditional`
	CONCEPT	`distinguishing_crossing_curves (info \| search),` `all (info \| search),` `on_line_or_curve (info \| search),` `outlined_filled (info \| search),` `shape_cluster (info \| search),` `cluster (info \| search),` `same_feature (info \| search),` `same (info \| search),` `texture (info \| search)`
	AUTHOR	`Harry E. Foundalis`

One protrusion and one indentation of the same shape vs. not so.

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

	CROSSREFS	`Adjacent-numbered pages: BP120 BP121 BP122 BP123 BP124 * BP126 BP127 BP128 BP129 BP130`
	KEYWORD	`traditional`
	CONCEPT	`indentation (info \| search),` `protrusion (info \| search),` `same_shape (info \| search),` `same (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

Considering only the ways they are connected, anything that can be said about a given edge can be said about every other edge vs. not so.

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

	REFERENCE	`https://mathworld.wolfram.com/Edge-TransitiveGraph.html`
	CROSSREFS	`Adjacent-numbered pages: BP1104 BP1105 BP1106 BP1107 BP1108 * BP1110 BP1111 BP1112 BP1113 BP1114`
	KEYWORD	`precise, allsorted, notso, math, left-narrow, preciseworld`
	CONCEPT	`graph (info \| search),` `distinguishing_crossing_curves (info \| search)`
	WORLD	`graph [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

Blank image vs. nothing.

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

	COMMENTS	`Two kinds of "nothing".`
	CROSSREFS	`See also BP1219, "blank image vs. image of blank square".` `Adjacent-numbered pages: BP1051 BP1052 BP1053 BP1054 BP1055 * BP1057 BP1058 BP1059 BP1060 BP1061`
	KEYWORD	`less, left-finite, right-finite, left-full, right-full, left-null, finished, invalid, experimental, funny, finishedexamples`
	CONCEPT	`empty (info \| search),` `existence (info \| search),` `zero (info \| search)`
	WORLD	`blank_image [smaller \| same \| bigger] zoom in left (blank_image) \| zoom in right (nothing)`
	AUTHOR	`Aaron David Fairbanks`

Sequence contains each possible way its distinct elements can be arranged as a subsequence vs. not so.

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

	REFERENCE	`https://en.wikipedia.org/wiki/Superpermutation`
	CROSSREFS	`Adjacent-numbered pages: BP1268 BP1269 BP1270 BP1271 BP1272 * BP1274 BP1275 BP1276 BP1277 BP1278`
	EXAMPLE	`There are 6 ways of arranging the letters A, B and C: ABC, ACB, BAC, BCA, CAB, and CBA. The string "ABCABACBA" contains each of these as a substring, and would therefore be sorted left.`
	KEYWORD	`precise, allsorted, notso, sequence, traditional, miniworlds`
	CONCEPT	`sequence (info \| search),` `overlap (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

Increasing quantity has no lower (or upper) bound (and gives a representation of negative numbers) vs. increasing quantity has lower bound.

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

	COMMENTS	`All left examples have a clear "zero" value, but it may be unclear which side is meant to be positive and which side is meant to be negative (See BP893^left for quantities without clear notion of increase/decrease.)`
	CROSSREFS	`See BP353^left for looping quantities; these do not clearly represent positive and negative numbers, but they can likewise unboundedly decrease and increase.` `See BP870 for a version about upper bounds.` `Adjacent-numbered pages: BP347 BP348 BP349 BP350 BP351 * BP353 BP354 BP355 BP356 BP357`
	KEYWORD	`creativeexamples, structure, sequence, traditional, rules`
	CONCEPT	`size_increase_decrease (info \| search),` `iteration (info \| search),` `tracing_line_or_curve (info \| search)`
	WORLD	`constant_change_seq_increase_right [smaller \| same \| bigger] zoom in right (constant_change_seq_increase_right_lower_bound)`
	AUTHOR	`Aaron David Fairbanks`

The left part has more pixels (area) than the right part vs. the left part has fewer pixels than the right part.

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

	CROSSREFS	`Adjacent-numbered pages: BP274 BP275 BP276 BP277 BP278 * BP280 BP281 BP282 BP283 BP284`
	KEYWORD	`dual, handed, leftright, pixelperfect`
	CONCEPT	`left_right (info \| search),` `length_line_or_curve (info \| search),` `area (info \| search)`
	WORLD	`arial_font_two_symbols [smaller \| same \| bigger]`
	AUTHOR	`Merse E. Gáspár`

No small square at the end of any curve vs. curve ends at a small square.

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

	CROSSREFS	`Adjacent-numbered pages: BP216 BP217 BP218 BP219 BP220 * BP222 BP223 BP224 BP225 BP226`
	KEYWORD	`less, traditional`
	CONCEPT	`existence (info \| search),` `curve_texture (info \| search),` `texture (info \| search)`
	AUTHOR	`Giuseppe Insana`

Left shapes can be placed on top of each other to make right shape vs. not so.

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

	CROSSREFS	`Adjacent-numbered pages: BP319 BP320 BP321 BP322 BP323 * BP325 BP326 BP327 BP328 BP329`
	KEYWORD	`precise, unstable, perfect, pixelperfect, structure, orderedtriplet, traditional`
	CONCEPT	`set_union (info \| search),` `same_shape (info \| search),` `same (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

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