The On-Line Encyclopedia of Bongard Problems

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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.

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

	CROSSREFS	`Adjacent-numbered pages: BP1264 BP1265 BP1266 BP1267 BP1268 *`
	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`

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`

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`
	KEYWORD	`precise, allsorted, notso, perfect`
	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`
	KEYWORD	`allsorted, notso, traditional`
	CONCEPT	`angle (info \| search),` `size_increase_decrease (info \| search)`
	AUTHOR	`Leo Crabbe`

BP1265

Visual Bongard Problems about unsorted collections of objects vs. other visual Bongard Problems.

	BP343	BP347	BP349	BP379	BP380	BP384
	BP792

?
BP824

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

	COMMENTS	`Left-sorted Bongard Problems have the keyword "collection" on the OEBP.` `A Problem is sorted left if its examples typically multiple objects, and the solution pertains to the way properties of the objects interrelate. If the positions of objects are relevant to the solution (see "sequence" Problems: BP929), then the Problem is sorted right.`
	CROSSREFS	`Adjacent-numbered pages: BP1260 BP1261 BP1262 BP1263 BP1264 * BP1266 BP1267 BP1268 BP1269`
	KEYWORD	`meta (see left/right), links, keyword`
	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`

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`

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`

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`

BP1260

Same transformation applied to circle, triangle, and square vs. different transformations applied.

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

	CROSSREFS	`BP839 is about applying opposite transformations to a single object.` `Adjacent-numbered pages: BP1255 BP1256 BP1257 BP1258 BP1259 * BP1261 BP1262 BP1263 BP1264 BP1265`
	KEYWORD	`easy, nice, abstract, arbitrary, anticomputer, left-null, structure, orderedtriplet, traditional, rules`
	CONCEPT	`circle (info \| search),` `analogy (info \| search),` `square (info \| search),` `same (info \| search),` `triangle (info \| search),` `function (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

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