The On-Line Encyclopedia of Bongard Problems

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BP1244

Tiled by self-tiling fractal vs. not

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	COMMENTS	`Proofs are still needed for examples fitting right.` `EX9875 is tiled by Sierpinski triangles, but this requires the Sierpinski triangle tiles' bounding triangles to overlap.`
	CROSSREFS	`Self-tiling fractals (BP532^left) are all sorted left.` `Adjacent-numbered pages: BP1239 BP1240 BP1241 BP1242 BP1243 * BP1245 BP1246 BP1247 BP1248 BP1249`
	KEYWORD	`notso, perfect, infinitedetail, missingproofs`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search),` `tiling (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.

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

	CROSSREFS	`Adjacent-numbered pages: BP1240 BP1241 BP1242 BP1243 BP1244 * BP1246 BP1247 BP1248 BP1249 BP1250`
	KEYWORD	`hard, precise, convoluted, dual, rotate, boundingbox, hardsort, challenge, proofsrequired`
	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.

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

	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	`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.

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

	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	`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`

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`
	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.

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

	CROSSREFS	`Adjacent-numbered pages: BP1247 BP1248 BP1249 BP1250 BP1251 * BP1253 BP1254`
	KEYWORD	`precise, allsorted, notso, blackwhite`
	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`
	KEYWORD	`experimental`
	AUTHOR	`Leo Crabbe`

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