The On-Line Encyclopedia of Bongard Problems

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BP115

Innermost shape is reachable from the outermost one vs. innermost shape is unreachable from the outermost one.

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	CROSSREFS	`Adjacent-numbered pages: BP110 BP111 BP112 BP113 BP114 * BP116 BP117 BP118 BP119 BP120`
	KEYWORD	`traditional`
	CONCEPT	`innermost_outermost (info \| search),` `path (info \| search),` `reachable (info \| search),` `tracing_line_or_curve (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

BP118

No cycle vs. a cycle exists.

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	CROSSREFS	`Adjacent-numbered pages: BP113 BP114 BP115 BP116 BP117 * BP119 BP120 BP121 BP122 BP123`
	KEYWORD	`traditional`
	CONCEPT	`arrow (info \| search),` `cyclic_path (info \| search),` `existence (info \| search),` `path (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

BP176

Line that connects dots avoiding obstacles is short vs. line that connects dots avoiding obstacles is long.

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	CROSSREFS	`Adjacent-numbered pages: BP171 BP172 BP173 BP174 BP175 * BP177 BP178 BP179 BP180 BP181`
	KEYWORD	`nice, spectrum, traditional, continuous`
	CONCEPT	`length_line_or_curve (info \| search),` `path (info \| search)`
	AUTHOR	`Harry E. Foundalis`

BP294

The two points are reachable through a path vs. the two points are unreachable by any path.

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	CROSSREFS	`Adjacent-numbered pages: BP289 BP290 BP291 BP292 BP293 * BP295 BP296 BP297 BP298 BP299`
	KEYWORD	`traditional`
	CONCEPT	`maze (info \| search),` `path (info \| search),` `reachable (info \| search)`
	AUTHOR	`"Lewis"`

BP314

Long distance between the marked locations vs. short distance between the marked locations.

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	CROSSREFS	`Adjacent-numbered pages: BP309 BP310 BP311 BP312 BP313 * BP315 BP316 BP317 BP318 BP319`
	KEYWORD	`traditional`
	CONCEPT	`length_line_or_curve (info \| search),` `maze (info \| search),` `path (info \| search)`
	AUTHOR	`Jakub Štepo`

BP316

At least one path is a cycle vs. no path is a cycle.

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	CROSSREFS	`Adjacent-numbered pages: BP311 BP312 BP313 BP314 BP315 * BP317 BP318 BP319 BP320 BP321`
	KEYWORD	`traditional`
	CONCEPT	`cyclic_path (info \| search),` `maze (info \| search),` `path (info \| search)`
	AUTHOR	`Jakub Štepo`

BP321

Small round object unreachable from the border of the box vs. small round object reachable from the border of the box.

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	COMMENTS	`Equivalently, "small round object enclosed by white loop vs. not so."`
	CROSSREFS	`Adjacent-numbered pages: BP316 BP317 BP318 BP319 BP320 * BP322 BP323 BP324 BP325 BP326`
	KEYWORD	`nice, precise, allsorted, boundingbox, perfect, pixelperfect, traditional, bordercontent`
	CONCEPT	`bounding_box (info \| search),` `path (info \| search),` `reachable (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP394

For each colored square only, there exists a path starting on it that covers each square of the figure exactly once vs. there is no path that starts on a colored square and covers each square of the figure exactly once.

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

	CROSSREFS	`Adjacent-numbered pages: BP389 BP390 BP391 BP392 BP393 * BP395 BP396 BP397 BP398 BP399`
	KEYWORD	`hard, nice, solved, traditional, dithering, left-listable, right-listable`
	CONCEPT	`existence (info \| search),` `path (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search)`
	AUTHOR	`Jago Collins`

BP997

There exists a loop that passes through every white square once without passing through the black square vs. there exists no such loop.

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	CROSSREFS	`Adjacent-numbered pages: BP992 BP993 BP994 BP995 BP996 * BP998 BP999 BP1000 BP1001 BP1002`
	KEYWORD	`precise, allsorted, grid, preciseworld, left-listable, right-listable`
	CONCEPT	`path (info \| search)`
	AUTHOR	`James Tanton`

BP1292

Requires an even number of paths to cover all black squares vs requires an odd number of paths to cover all black squares

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	COMMENTS	`A path is formally defined as a sequence of black squares such that no two squares are the same and every pair of consecutive black squares are orthogonally adjacent to each other.` `Every grid on the left requires a minimum of an even number of paths such that every black square is a part of exactly one path, while every grid on the right requires a minimum of an odd number of paths to do so.`
	CROSSREFS	`Adjacent-numbered pages: BP1287 BP1288 BP1289 BP1290 BP1291 * BP1293 BP1294 BP1295`
	EXAMPLE	`A grid with all whites fits on the left because it does not contain black squares, hence requiring 0 paths, an even number.` `A grid with all blacks requires 1 path to go through all black squares (such as a zigzag through every row), an odd number.` `The checkerboard grid on the left contains 12 black squares that cannot be joined with a path, hence it requires 12 paths, an even number.`
	KEYWORD	`nice, blackwhite, fixedgrid, left-listable, right-listable`
	CONCEPT	`path (info \| search)`
	AUTHOR	`Matt Nguyen`

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