The On-Line Encyclopedia of Bongard Problems

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

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	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`

BP1246

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

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	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.

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	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.

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	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`

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.

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	COMMENTS	`Any palindrome would be sorted left, except strings of length zero or one.`
	CROSSREFS	`Adjacent-numbered pages: BP1263 BP1264 BP1265 BP1266 BP1267 * BP1269 BP1270 BP1271 BP1272 BP1273`
	KEYWORD	`precise, allsorted, unwordable, notso, sequence, traditional, miniworlds`
	CONCEPT	`element_wise_symmetry (info \| search),` `element_grouping (info \| search),` `sequence (info \| search),` `same_shape (info \| search),` `same (info \| search)`
	WORLD	`[smaller \| same \| bigger] zoom in left \| zoom in right`
	AUTHOR	`Leo Crabbe`

BP1271

Positive correlation vs. negative correlation.

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	COMMENTS	`All examples in this Bongard Problem are scatter plots. Each dot represents a data point.` `"Positive correlation" means that when the X value increases, the Y value tends to increase as well (in the long run), while "negative correlation" means that when the X value increases, the Y value tends to decrease.`
	CROSSREFS	`Adjacent-numbered pages: BP1266 BP1267 BP1268 BP1269 BP1270 * BP1272 BP1273 BP1274 BP1275 BP1276`
	EXAMPLE	`Example TM4854 does not fit on either side because when the X value increases, the Y value stays the same.` `Example TM4855 does not fit on either side because there is no correlation.`
	KEYWORD	`fuzzy, minimal, unwordable, teach, spectrum, dual, handed, leftright, updown, rotate, stable, hardsort, left-narrow, right-narrow`
	AUTHOR	`Ben`

BP1275

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`

BP1276

Ways of representing the sequence "ABABCBACCBAC" by grouping its elements into equal-sized blocks and relabelling them (identical blocks are represented by the same element) vs. representations of different sequences.

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	COMMENTS	`The solver isn't expected to word their solution as it is put above, but to notice that the sequences on the left all "agree" with each other under the aforementioned grouping rule. The 12-element sequence in EX10249 can be "squashed down" into the 6-element sequence in EX10251, which in turn can be "squashed down" into the 3-element sequence in EX10252.`
	CROSSREFS	`Compare to BP121` `Adjacent-numbered pages: BP1271 BP1272 BP1273 BP1274 BP1275 * BP1277 BP1278 BP1279 BP1280 BP1281`
	KEYWORD	`unwordable, notso, arbitrary, sequence`
	CONCEPT	`element_grouping (info \| search)`
	AUTHOR	`Leo Crabbe`

BP1279

Circled points are all possible vertices a square with a particular side length can take, provided that each of its corners lie on a grid point vs. not so.

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	COMMENTS	`Rotation of the square is allowed.`
	CROSSREFS	`See BP1280 for version with hexagons on a hexagonal grid.` `Adjacent-numbered pages: BP1274 BP1275 BP1276 BP1277 BP1278 * BP1280 BP1281 BP1282 BP1283 BP1284`
	KEYWORD	`hard, precise, allsorted, unwordable, hardsort, left-finite, right-finite, left-full, fixedgrid, preciseworld`
	CONCEPT	`square (info \| search)`
	AUTHOR	`Leo Crabbe`

BP1280

Circled points are all possible vertices a regular hexagon with a particular side length can take, provided that each of its corners lie on a grid point vs. not so.