The On-Line Encyclopedia of Bongard Problems

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Equal number of black and white pixels vs. not

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	CROSSREFS	`Adjacent-numbered pages: BP1084 BP1085 BP1086 BP1087 BP1088 * BP1090 BP1091 BP1092 BP1093 BP1094`
	KEYWORD	`nice, precise, allsorted, boundingbox, right-null, perfect, pixelperfect, help, preciseworld, bordercontent, blackwhiteinvariant`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Jago Collins`

BP1093

"Inverted symmetry" present vs. not

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	CROSSREFS	`Adjacent-numbered pages: BP1088 BP1089 BP1090 BP1091 BP1092 * BP1094 BP1095 BP1096 BP1097 BP1098`
	KEYWORD	`nice, precise, allsorted, boundingbox, left-narrow, right-null, perfect, pixelperfect, preciseworld, bordercontent, blackwhiteinvariant`
	CONCEPT	`black_white_inversion (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Jago Collins`

BP1228

Frieze pattern with glide reflection symmetry vs. not.

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	COMMENTS	`Each example on the left is imagined to continue beyond the bounding box.`
	CROSSREFS	`Adjacent-numbered pages: BP1223 BP1224 BP1225 BP1226 BP1227 * BP1229 BP1230 BP1231 BP1232 BP1233`
	KEYWORD	`stub, notso, traditional, bordercontent, seemslike`
	CONCEPT	`symmetry (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP1230

Invariant under scaling by a certain amount vs. not.

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	COMMENTS	`Each example on the left is imagined to continue beyond the bounding box.`
	CROSSREFS	`Adjacent-numbered pages: BP1225 BP1226 BP1227 BP1228 BP1229 * BP1231 BP1232 BP1233 BP1234 BP1235`
	KEYWORD	`stub, notso, perfect, infinitedetail, left-couldbe, bordercontent, blackwhiteinvariant`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `symmetry (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP1245

When two players alternate coloring regions, either can force connection from top edge to bottom edge vs. either can force connection from left edge to right edge.

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	REFERENCE	`https://en.wikipedia.org/wiki/Hex_(board_game)`
	CROSSREFS	`Adjacent-numbered pages: BP1240 BP1241 BP1242 BP1243 BP1244 * BP1246 BP1247 BP1248 BP1249 BP1250`
	KEYWORD	`hard, precise, convoluted, dual, rotate, boundingbox, hardsort, challenge, proofsrequired, bordercontent`
	AUTHOR	`Aaron David Fairbanks`

BP1249

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

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	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.

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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`

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