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`

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`

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`

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`
	KEYWORD	`precise, allsorted, notso, perfect`
	AUTHOR	`Leo Crabbe`

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