The On-Line Encyclopedia of Bongard Problems

Search: user:Leo Crabbe

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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`

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`

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`

BP1263

Uncategorizable images vs. categorizable images.

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

	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.

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

	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`

BP1255

Shades of green vs. shades of red.

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

	CROSSREFS	`Adjacent-numbered pages: BP1250 BP1251 BP1252 BP1253 BP1254 * BP1256 BP1257 BP1258 BP1259 BP1260`
	KEYWORD	`easy, precise, allsorted, minimal, arbitrary, color, continuous`
	AUTHOR	`Leo Crabbe`

BP1253

Text strings vs. images of text strings

WWWWWWW

____hem

image

joym

жю

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

	CROSSREFS	`Adjacent-numbered pages: BP1248 BP1249 BP1250 BP1251 BP1252 * BP1254 BP1255 BP1256 BP1257 BP1258`
	KEYWORD	`gap, experimental`
	AUTHOR	`Leo Crabbe`

BP1252

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

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	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`

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`

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