The On-Line Encyclopedia of Bongard Problems

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Shapes are sorted according to a simple rule that uniquely determines where everything goes vs. shapes are sorted according to some other rule (or lack thereof).

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	CROSSREFS	`Adjacent-numbered pages: BP1150 BP1151 BP1152 BP1153 BP1154 * BP1156 BP1157 BP1158 BP1159 BP1160`
	KEYWORD	`abstract, unwordable, creativeexamples, right-unknowable, traditional, finishedexamples, rules`
	AUTHOR	`Leo Crabbe`

BP1157

The order in which the objects in the top half are combined to make the object in the lower half matters vs. not so.

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	COMMENTS	`Operations depicted in right-sorted examples are called "commutative".` `"Order matters" here means that if the objects in the top half were to switch places, the output would look different.`
	REFERENCE	`https://en.wikipedia.org/wiki/Commutative_property`
	CROSSREFS	`Adjacent-numbered pages: BP1152 BP1153 BP1154 BP1155 BP1156 * BP1158 BP1159 BP1160 BP1161 BP1162`
	KEYWORD	`nice, abstract, unwordable, notso, structure, rules, miniworlds`
	CONCEPT	`function (info \| search)`
	AUTHOR	`Leo Crabbe`

BP1161

Image contains the exact arrangement of pixels that form the "S" creature depicted in EX9532 vs. not so.

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

	CROSSREFS	`Adjacent-numbered pages: BP1156 BP1157 BP1158 BP1159 BP1160 * BP1162 BP1163 BP1164 BP1165 BP1166`
	KEYWORD	`unwordable, notso, arbitrary, handed, leftright, updown, stretch, blackwhite, creativeexamples, right-null, perfect, pixelperfect, help`
	AUTHOR	`Leo Crabbe`

BP1181

Unordered object-wise comparison Bongard Problems where the number of objects can vary between examples vs. similar Bongard Problems where certain objects are distinguishable in some consistent way across all examples.

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	COMMENTS	`Any "sequence" (BP929^left) or "grid" (BP1176^left) Problems will be sorted right.`
	CROSSREFS	`Adjacent-numbered pages: BP1176 BP1177 BP1178 BP1179 BP1180 * BP1182 BP1183 BP1184 BP1185 BP1186`
	KEYWORD	`unwordable, meta (see left/right), links`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP1246

Any symmetry exhibited by some non-empty subset of the objects is also a symmetry of the whole thing vs. not so.

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

	COMMENTS	`In other words, placing the image over itself (rotation and flipping allowed) so that any parts match up makes the whole image match up to itself vs. not so.`
	CROSSREFS	`See BP965 for a variation on this idea where the "parts" are allowed to be arbitrary regions of the image instead of individual objects shown in the image.` `Adjacent-numbered pages: BP1241 BP1242 BP1243 BP1244 BP1245 * BP1247 BP1248 BP1249 BP1250 BP1251`
	KEYWORD	`precise, allsorted, unwordable, notso, traditional`
	CONCEPT	`local_global (info \| search),` `self-reference (info \| search),` `symmetry (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP1247

No straight path from one side of the panel to the other passes through the grey shape without hitting a black region vs. such a path exists.

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

	REFERENCE	`https://en.wikipedia.org/wiki/Opaque_set`
	CROSSREFS	`Adjacent-numbered pages: BP1242 BP1243 BP1244 BP1245 BP1246 * BP1248 BP1249 BP1250 BP1251 BP1252`
	KEYWORD	`precise, allsorted, unwordable, notso`
	CONCEPT	`imagined_line_or_curve (info \| search)`
	WORLD	`[smaller \| same \| bigger] zoom in left`
	AUTHOR	`Leo Crabbe`

BP1248

No straight path passes from a white region to a grey one, then to white again (without hitting black) vs. such a path exists.

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

	CROSSREFS	`Any small amount of convexity along the grey border will cause an example to fit right.` `Adjacent-numbered pages: BP1243 BP1244 BP1245 BP1246 BP1247 * BP1249 BP1250 BP1251 BP1252 BP1253`
	KEYWORD	`precise, allsorted, unwordable, notso, perfect`
	CONCEPT	`imagined_line_or_curve (info \| search)`
	WORLD	`[smaller \| same \| bigger] zoom in left`
	AUTHOR	`Leo Crabbe`

BP1250

BPs whose left-sorted examples exhibit the following property: if a square region of any left-sorted example is replaced with any other left-sorted example, the resultant image is also sorted left vs. BPs whose left-sorted examples do not exhibit this property.

BP1

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

	CROSSREFS	`Adjacent-numbered pages: BP1245 BP1246 BP1247 BP1248 BP1249 * BP1251 BP1252 BP1253 BP1254 BP1255`
	KEYWORD	`unwordable, meta (see left/right), links`
	AUTHOR	`Leo Crabbe`

BP1251

BPs whose right-sorted examples exhibit the following property: if a square region of any right-sorted example is replaced with any other right-sorted example, the resultant image is also sorted right vs. BPs whose right-sorted examples do not exhibit this property.

BP1

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

	CROSSREFS	`Adjacent-numbered pages: BP1246 BP1247 BP1248 BP1249 BP1250 * BP1252 BP1253 BP1254 BP1255 BP1256`
	KEYWORD	`unwordable, meta (see left/right), links`
	AUTHOR	`Leo Crabbe`

BP1268

Palindromic when elements are grouped into (more than one) equal-sized blocks vs. no grouping of elements into (more than one) equal-sized blocks is palindromic.

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

	COMMENTS	`Any palindrome would be sorted left, except strings of length zero or one.`
	CROSSREFS	`Adjacent-numbered pages: BP1263 BP1264 BP1265 BP1266 BP1267 * BP1269`
	KEYWORD	`precise, allsorted, unwordable, sequence, traditional, miniworlds`
	CONCEPT	`element_wise_symmetry (info \| search),` `sequence (info \| search),` `same_shape (info \| search),` `same (info \| search)`
	WORLD	`zoom in left \| zoom in right`
	AUTHOR	`Leo Crabbe`

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