The On-Line Encyclopedia of Bongard Problems

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There exists an edge such that removing it yields two disconnected graphs (i.e., the minimum number of edges whose removal results in two disconnected graphs is 1) vs. the minimum number of edges whose removal results in two disconnected graphs is 2.

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	CROSSREFS	`Adjacent-numbered pages: BP386 BP387 BP388 BP389 BP390 * BP392 BP393 BP394 BP395 BP396`
	KEYWORD	`nice, precise, traditional, preciseworld`
	CONCEPT	`graph (info \| search),` `distinguishing_crossing_curves (info \| search),` `existence (info \| search),` `imagined_shape (info \| search),` `imagined_entity (info \| search)`
	WORLD	`connected_graph [smaller \| same \| bigger]`
	AUTHOR	`Jago Collins`

BP390

Each graph vertex is uniquely defined by its connections (the graph does not admit nontrivial automorphisms) vs. the graph admits nontrivial automorphisms.

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	CROSSREFS	`Adjacent-numbered pages: BP385 BP386 BP387 BP388 BP389 * BP391 BP392 BP393 BP394 BP395`
	KEYWORD	`precise, allsorted, notso, traditional, preciseworld`
	CONCEPT	`graph (info \| search),` `self-reference (info \| search),` `topological_transformation (info \| search),` `imagined_shape (info \| search),` `imagined_entity (info \| search)`
	WORLD	`connected_graph [smaller \| same \| bigger]`
	AUTHOR	`Jago Collins`

BP389

Loops are entangled (in 3-D) vs. loops can be separated (in 3-D).

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	CROSSREFS	`Adjacent-numbered pages: BP384 BP385 BP386 BP387 BP388 * BP390 BP391 BP392 BP393 BP394`
	KEYWORD	`nice, precise, allsorted, contributepairs, traditional`
	CONCEPT	`knot (info \| search),` `topological_transformation (info \| search),` `imagined_motion (info \| search),` `motion (info \| search)`
	WORLD	`link_two_knots [smaller \| same \| bigger]`
	AUTHOR	`Jago Collins`

BP388

White dot can see (in straight lines) all black points vs. white dot cannot see (in straight lines) all black points.

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	CROSSREFS	`See BP368 for whether ALL points can see all points.` `Adjacent-numbered pages: BP383 BP384 BP385 BP386 BP387 * BP389 BP390 BP391 BP392 BP393`
	KEYWORD	`nice, traditional`
	CONCEPT	`all (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search)`
	WORLD	`fill_shape_white_dot [smaller \| same \| bigger]`
	AUTHOR	`Jago Collins`

BP387

Dots can be shared equally between figures vs. dots cannot be shared equally between figures.

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	CROSSREFS	`Adjacent-numbered pages: BP382 BP383 BP384 BP385 BP386 * BP388 BP389 BP390 BP391 BP392`
	KEYWORD	`nice, traditional`
	CONCEPT	`division (info \| search)`
	AUTHOR	`Jago Collins`

BP386

Lower shape can be used as a tile to build the upper one vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP381 BP382 BP383 BP384 BP385 * BP387 BP388 BP389 BP390 BP391`
	KEYWORD	`nice, precise, allsorted, left-narrow, perfect, pixelperfect, orderedpair, traditional, preciseworld, left-listable, right-listable`
	CONCEPT	`tiling (info \| search)`
	AUTHOR	`Jago Collins`

BP385

Nets of cubes vs. not nets of cubes.

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	CROSSREFS	`Adjacent-numbered pages: BP380 BP381 BP382 BP383 BP384 * BP386 BP387 BP388 BP389 BP390`
	KEYWORD	`nice, notso, left-finite, traditional`
	CONCEPT	`3d_net (info \| search)`
	WORLD	`square_outlines_sharing_edges [smaller \| same \| bigger] zoom in left (cube_net)`
	AUTHOR	`Jago Collins`

BP384

Square number of dots vs. non-square number of dots.

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	COMMENTS	`All examples in this Problem are a collection of dots.` `An equivalent solution is "Dots can be arranged into a square lattice whose convex hull is a square vs. not so". - Leo Crabbe, Aug 01 2020`
	CROSSREFS	`Adjacent-numbered pages: BP379 BP380 BP381 BP382 BP383 * BP385 BP386 BP387 BP388 BP389`
	EXAMPLE	`A single dot fits because 1 = 11.` `A pair of dots does not fit because there is no integer x such that 2 = xx.`
	KEYWORD	`nice, precise, allsorted, number, math, left-narrow, left-null, help, traditional, preciseworld, collection`
	CONCEPT	`square_number (info \| search)`
	WORLD	`dots [smaller \| same \| bigger]`
	AUTHOR	`Jago Collins`

BP383

When the shape is removed from the dots, the dots give enough information to place the shape back where it was vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP378 BP379 BP380 BP381 BP382 * BP384 BP385 BP386 BP387 BP388`
	KEYWORD	`hard, nice, traditional`
	CONCEPT	`imagined_line_or_curve (info \| search),` `imagined_entity (info \| search),` `convey_enough_information (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP382

No knot (unknot) vs. knot.

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	COMMENTS	`To hint at the solution, left examples can be arranged in a sequence to show the unknot tying itself.`
	CROSSREFS	`Adjacent-numbered pages: BP377 BP378 BP379 BP380 BP381 * BP383 BP384 BP385 BP386 BP387`
	KEYWORD	`nice, math, anticomputer, help, traditional`
	CONCEPT	`knot (info \| search),` `topological_transformation (info \| search)`
	WORLD	`knot [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

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