The On-Line Encyclopedia of Bongard Problems

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BP188

Shape of whole different from shape of parts vs. shape of whole same as shape of parts.

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

	CROSSREFS	`See BP1002 for more general visual self-similarity.` `See BP1064 for a similar Problem about two shapes inter-referencing instead of just one shape referencing itself.` `Adjacent-numbered pages: BP183 BP184 BP185 BP186 BP187 * BP189 BP190 BP191 BP192 BP193`
	KEYWORD	`traditional`
	CONCEPT	`recursion (info \| search),` `self-reference (info \| search),` `similar_shape (info \| search),` `similar (info \| search)`
	AUTHOR	`Harry E. Foundalis`

BP1138

Each attribute is shared by every group or none vs. some attribute is shared by exactly two groups

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

	COMMENTS	`Attributes are shading, shape, and number.` `There are always three groups.` `This problem is related to the card game Set.`
	CROSSREFS	`Adjacent-numbered pages: BP1133 BP1134 BP1135 BP1136 BP1137 * BP1139 BP1140 BP1141 BP1142 BP1143`
	KEYWORD	`nice, precise, allsorted, notso, preciseworld`
	CONCEPT	`all (info \| search),` `number (info \| search),` `same (info \| search),` `two (info \| search),` `three (info \| search)`
	AUTHOR	`William B Holland`

BP146

A shape contains a square if and only if it is a circle vs. a shape contains a square if and only if it is a triangle.

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

	CROSSREFS	`Adjacent-numbered pages: BP141 BP142 BP143 BP144 BP145 * BP147 BP148 BP149 BP150 BP151`
	KEYWORD	`traditional`
	CONCEPT	`iff (info \| search),` `inside (info \| search),` `triangle (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

BP904

Rows show all possible ways a certain number of dots can be divided between a certain number of bins vs. not so.

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

	COMMENTS	`The rows in the panels on the right hand side show all the ways you can divide a certain number of dots between a certain number of bins, ignoring which bins they are placed in.`
	CROSSREFS	`Adjacent-numbered pages: BP899 BP900 BP901 BP902 BP903 * BP905 BP906 BP907 BP908 BP909`
	KEYWORD	`solved, left-null, grid, left-listable, right-listable`
	CONCEPT	`permutation (info \| search)`
	AUTHOR	`Molly C Klenzak`

BP190

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`

BP125

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`

BP1109

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`

BP1056

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`

BP1273

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`

BP352

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`

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