The On-Line Encyclopedia of Bongard Problems

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BP1249

Any straight path will hit a black region vs. not so.

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

	REFERENCE	`https://en.wikipedia.org/wiki/Opaque_set`
	CROSSREFS	`Adjacent-numbered pages: BP1244 BP1245 BP1246 BP1247 BP1248 * BP1250 BP1251 BP1252 BP1253 BP1254`
	KEYWORD	`notso, blackwhite, right-null, perfect, bordercontent`
	CONCEPT	`imagined_line_or_curve (info \| search)`
	AUTHOR	`Leo Crabbe`

BP1252

No entirely white paths from one side to another vs. one can find such a path.

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

	COMMENTS	`The left-sorted patterns connect all four corners with a single black region. - Rhodri Prysor, Oct 16 2024`
	CROSSREFS	`Adjacent-numbered pages: BP1247 BP1248 BP1249 BP1250 BP1251 * BP1253 BP1254 BP1255 BP1256 BP1257`
	KEYWORD	`precise, allsorted, notso, blackwhite, right-null, bordercontent`
	AUTHOR	`Leo Crabbe`

BP1258

It is possible to deduce the contents of any square from the rest vs. it is not.

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	CROSSREFS	`BP979 is very similar: whether a particular square can be deduced from the rest.` `Adjacent-numbered pages: BP1253 BP1254 BP1255 BP1256 BP1257 * BP1259 BP1260 BP1261 BP1262 BP1263`
	KEYWORD	`notso, rules, grid, miniworlds`
	CONCEPT	`convey_enough_information (info \| search),` `choice (info \| search)`
	WORLD	`grid_of_images_with_rule [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1259

Rule is the same for rows as it is for columns vs. not

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	CROSSREFS	`All examples on the left are chosen so that rotating or flipping the grid in any way would result in a grid satisfying the same rule.` `Adjacent-numbered pages: BP1254 BP1255 BP1256 BP1257 BP1258 * BP1260 BP1261 BP1262 BP1263 BP1264`
	KEYWORD	`notso, rules, grid, miniworlds`
	WORLD	`grid_of_images_with_rule [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1261

Exactly one connected white region for each possible way shapes can overlap vs. not so.

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

	COMMENTS	`All left-sorted examples have 2^n distinct white regions (counting the background), where n is the number of shapes in the image.`
	REFERENCE	`https://en.wikipedia.org/wiki/Venn_diagram`
	CROSSREFS	`Similar solution to BP1262, except there overlaps do not have to be unique.` `Adjacent-numbered pages: BP1256 BP1257 BP1258 BP1259 BP1260 * BP1262 BP1263 BP1264 BP1265 BP1266`
	KEYWORD	`notso, left-narrow, left-null, perfect`
	CONCEPT	`exists_one (info \| search)`
	AUTHOR	`Leo Crabbe`

BP1264

Any shape's axis of reflection is shared by another shape vs. not so.

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

	CROSSREFS	`Adjacent-numbered pages: BP1259 BP1260 BP1261 BP1262 BP1263 * BP1265 BP1266 BP1267 BP1268 BP1269`
	KEYWORD	`precise, allsorted, notso, left-narrow`
	CONCEPT	`symmetry (info \| search)`
	AUTHOR	`Leo Crabbe`

BP1266

Angles either only increase or only decrease as one moves along the curve vs. not so.

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

	COMMENTS	`It does not matter which end of the curve one starts from, nor which "side" angles are measured from, so long as the side is kept consistent.`
	CROSSREFS	`Adjacent-numbered pages: BP1261 BP1262 BP1263 BP1264 BP1265 * BP1267 BP1268 BP1269 BP1270 BP1271`
	KEYWORD	`allsorted, notso, traditional`
	CONCEPT	`angle (info \| search),` `size_increase_decrease (info \| search)`
	AUTHOR	`Leo Crabbe`

BP1267

Any two lines intersect, and no three lines share an intersection point vs. not so.

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

	COMMENTS	`Left-sorted examples divide the plane into a maximal amount of disconnected white regions by a given number of "cuts". The number of regions in one of these examples will be the nth value of of the Lazy Caterer sequence ( https://oeis.org/A000124 ), where n is the number of lines.`
	REFERENCE	`https://en.wikipedia.org/wiki/Lazy_caterer%27s_sequence`
	CROSSREFS	`Adjacent-numbered pages: BP1262 BP1263 BP1264 BP1265 BP1266 * BP1268 BP1269 BP1270 BP1271 BP1272`
	KEYWORD	`precise, allsorted, notso, perfect`
	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 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`

BP1270

Straight line can separate the two types of figures vs. not so.

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

	COMMENTS	`This Bongard Problem is a sort of meta-problem. The problems inside the boxes aren't exactly Bongard problems, but they do deal with categorization. The objects must be split into two obvious and distinct groups, but one is not given any examples to work with.`
	CROSSREFS	`The two sides of BP3 are the same as the two sides in the first box.` `Adjacent-numbered pages: BP1265 BP1266 BP1267 BP1268 BP1269 * BP1271 BP1272 BP1273 BP1274 BP1275`
	KEYWORD	`notso`
	AUTHOR	`Ben`

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