The On-Line Encyclopedia of Bongard Problems

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

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	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`

BP1262

Shapes overlap in every possible way vs. not so.

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	COMMENTS	`Similar solution to BP1261, except overlaps do not have to be unique.`
	CROSSREFS	`Adjacent-numbered pages: BP1257 BP1258 BP1259 BP1260 BP1261 * BP1263 BP1264 BP1265 BP1266 BP1267`
	KEYWORD	`precise, left-null`
	AUTHOR	`Leo Crabbe`

BP1263

Uncategorizable images vs. categorizable images.

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	CROSSREFS	`Adjacent-numbered pages: BP1258 BP1259 BP1260 BP1261 BP1262 * BP1264 BP1265 BP1266 BP1267 BP1268`
	KEYWORD	`overriddensolution, left-finite, left-full, right-null, invalid, impossible, funny`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP1264

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

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	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.

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	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.

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	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.

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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`

BP1269

Identical pairs of symbols are always on opposite sides of the cube (when assembled) vs. some identical symbols are next to each other on the cube.

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	CROSSREFS	`Adjacent-numbered pages: BP1264 BP1265 BP1266 BP1267 BP1268 * BP1270 BP1271 BP1272 BP1273 BP1274`
	KEYWORD	`left-finite, right-finite, finishedexamples, preciseworld`
	CONCEPT	`cube (info \| search),` `correspondence (info \| search),` `3d_net (info \| search),` `3d_solid (info \| search)`
	AUTHOR	`Leo Crabbe`

BP1270

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

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	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`

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`

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