The On-Line Encyclopedia of Bongard Problems

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More triangles left than right vs. more triangles right than left.

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	COMMENTS	`The triangles vary in size in order to make the solution clearly about quantity, not "total mass".`
	CROSSREFS	`Adjacent-numbered pages: BP1203 BP1204 BP1205 BP1206 BP1207 * BP1209 BP1210 BP1211 BP1212 BP1213`
	KEYWORD	`stub, precise, spectrum, dual, handed, leftright, traditional`
	CONCEPT	`number (info \| search),` `triangle (info \| search),` `quantity_comparison (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP1212

Shape tiles a square vs. not

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	CROSSREFS	`Adjacent-numbered pages: BP1207 BP1208 BP1209 BP1210 BP1211 * BP1213 BP1214 BP1215 BP1216 BP1217`
	KEYWORD	`precise`
	WORLD	`fill_shape [smaller \| same \| bigger]`
	AUTHOR	`Jago Collins`

BP1216

Arrow pointing north-west vs. arrow pointing south-east.

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	CROSSREFS	`BP1218 is "arrow pointing north-west vs. arrow pointing elsewhere".` `Adjacent-numbered pages: BP1211 BP1212 BP1213 BP1214 BP1215 * BP1217 BP1218 BP1219 BP1220 BP1221`
	KEYWORD	`stub, precise, dual, handed, leftright, updown, rotate, left-narrow, right-narrow, traditional`
	CONCEPT	`diagonal (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP1218

Arrow pointing north-west vs. arrow pointing elsewhere.

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	CROSSREFS	`BP1216 is "arrow pointing north-west vs. arrow pointing south-east".` `Adjacent-numbered pages: BP1213 BP1214 BP1215 BP1216 BP1217 * BP1219 BP1220 BP1221 BP1222 BP1223`
	KEYWORD	`stub, precise, allsorted, notso, handed, leftright, updown, rotate, left-narrow, traditional`
	CONCEPT	`diagonal (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP1222

Same shape up to resizing vs. different shapes.

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	CROSSREFS	`BP57 instead requires the shapes are identical, even in size.` `Adjacent-numbered pages: BP1217 BP1218 BP1219 BP1220 BP1221 * BP1223 BP1224 BP1225 BP1226 BP1227`
	KEYWORD	`stub, precise, allsorted, traditional`
	CONCEPT	`size (info \| search),` `same_shape (info \| search),` `same (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP1227

Appears on its own right side vs. does not.

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	COMMENTS	`This was created as an example of a Bongard Problem that could include an image of a Bongard Problem with the same solution as itself but could not include the very image of itself (appearing within itself fractally).`
	CROSSREFS	`See also BP961, "appears on its own left side vs. appears on its own right side".` `Adjacent-numbered pages: BP1222 BP1223 BP1224 BP1225 BP1226 * BP1228 BP1229 BP1230 BP1231 BP1232`
	KEYWORD	`stub, precise, allsorted, notso, handed, leftright, example, perfect, infinitedetail`
	CONCEPT	`fractal (info \| search),` `recursion (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`

BP1246

Any symmetry exhibited by some non-empty subset of the objects is also a symmetry of the whole thing vs. not so.

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	COMMENTS	`In other words, placing the image over itself (rotation and flipping allowed) so that any parts match up makes the whole image match up to itself vs. not so.`
	CROSSREFS	`See BP965 for a variation on this idea where the "parts" are allowed to be arbitrary regions of the image instead of individual objects shown in the image.` `Adjacent-numbered pages: BP1241 BP1242 BP1243 BP1244 BP1245 * BP1247 BP1248 BP1249 BP1250 BP1251`
	KEYWORD	`precise, allsorted, unwordable, notso, traditional`
	CONCEPT	`local_global (info \| search),` `self-reference (info \| search),` `symmetry (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP1247

No straight path from one side of the panel to the other passes through the grey shape without hitting a black region vs. such a path exists.

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	REFERENCE	`https://en.wikipedia.org/wiki/Opaque_set`
	CROSSREFS	`Adjacent-numbered pages: BP1242 BP1243 BP1244 BP1245 BP1246 * BP1248 BP1249 BP1250 BP1251 BP1252`
	KEYWORD	`precise, allsorted, unwordable, notso`
	CONCEPT	`imagined_line_or_curve (info \| search)`
	WORLD	`[smaller \| same \| bigger] zoom in left`
	AUTHOR	`Leo Crabbe`

BP1248

No straight path passes from a white region to a grey one, then to white again (without hitting black) vs. such a path exists.

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

	CROSSREFS	`Any small amount of convexity along the grey border will cause an example to fit right.` `Adjacent-numbered pages: BP1243 BP1244 BP1245 BP1246 BP1247 * BP1249 BP1250 BP1251 BP1252 BP1253`
	KEYWORD	`precise, allsorted, unwordable, notso, perfect`
	CONCEPT	`imagined_line_or_curve (info \| search)`
	WORLD	`[smaller \| same \| bigger] zoom in left`
	AUTHOR	`Leo Crabbe`

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