The On-Line Encyclopedia of Bongard Problems

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BP525

Some zoomed-in (cropped) version of an image of a hollow circle vs. not so.

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

	CROSSREFS	`Adjacent-numbered pages: BP520 BP521 BP522 BP523 BP524 * BP526 BP527 BP528 BP529 BP530`
	KEYWORD	`stretch, boundingbox, left-null, traditional, left-couldbe`
	CONCEPT	`circle (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP527

Each black filled circle belongs to exactly one large circle outline vs. not so.

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

	COMMENTS	`On the left, circles define a partition of the dots.`
	CROSSREFS	`Adjacent-numbered pages: BP522 BP523 BP524 BP525 BP526 * BP528 BP529 BP530 BP531 BP532`
	KEYWORD	`precise, allsorted, traditional`
	CONCEPT	`circle (info \| search),` `exists_one (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP536

All gears can make complete turns vs. not so.

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

	CROSSREFS	`See BP336 for one gear turns all.` `Adjacent-numbered pages: BP531 BP532 BP533 BP534 BP535 * BP537 BP538 BP539 BP540 BP541`
	KEYWORD	`stretch, physics, traditional`
	CONCEPT	`all (info \| search),` `gear (info \| search)`
	WORLD	`gears [smaller \| same \| bigger] zoom in left \| zoom in right`
	AUTHOR	`Aaron David Fairbanks`

BP560

There exists a closed trail that hits each edge exactly once vs. not so.

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

	COMMENTS	`Left examples are called "Eulerian graphs."` `A connected graph is Eulerian if and only if each vertex is incident to an even number of edges.`
	CROSSREFS	`Adjacent-numbered pages: BP555 BP556 BP557 BP558 BP559 * BP561 BP562 BP563 BP564 BP565`
	KEYWORD	`precise, allsorted, math, traditional, preciseworld`
	CONCEPT	`graph (info \| search),` `distinguishing_crossing_curves (info \| search),` `all (info \| search),` `even_odd (info \| search),` `existence (info \| search)`
	WORLD	`connected_graph [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP562

There exists a closed trail that hits each vertex exactly once vs. not so.

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

	COMMENTS	`Left examples are called "Hamiltonian graphs."`
	CROSSREFS	`Adjacent-numbered pages: BP557 BP558 BP559 BP560 BP561 * BP563 BP564 BP565 BP566 BP567`
	KEYWORD	`math, traditional`
	CONCEPT	`graph (info \| search),` `distinguishing_crossing_curves (info \| search)`
	WORLD	`connected_graph [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP576

Vertices may be partitioned into two sets such that no two vertices in the same set are connected versus not so.

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

	COMMENTS	`Left examples are called "bipartite graphs."`
	CROSSREFS	`Adjacent-numbered pages: BP571 BP572 BP573 BP574 BP575 * BP577 BP578 BP579 BP580 BP581`
	KEYWORD	`precise, allsorted, notso, math, traditional, preciseworld`
	CONCEPT	`graph (info \| search),` `distinguishing_crossing_curves (info \| search)`
	WORLD	`graph [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP788

Graph contains a "loop" a.k.a. cycle (cyclic) versus graph is acyclic.

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

	CROSSREFS	`Adjacent-numbered pages: BP783 BP784 BP785 BP786 BP787 * BP789 BP790 BP791 BP792 BP793`
	KEYWORD	`nice, precise, allsorted, math, traditional, preciseworld`
	CONCEPT	`graph (info \| search),` `distinguishing_crossing_curves (info \| search),` `loop (info \| search)`
	WORLD	`connected_graph [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP790

The leftmost two add (as vectors) to the right versus no two add to a third.

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

	CROSSREFS	`Adjacent-numbered pages: BP785 BP786 BP787 BP788 BP789 * BP791 BP792 BP793 BP794 BP795`
	KEYWORD	`math, structure, orderedtriplet, traditional`
	CONCEPT	`addition (info \| search),` `2_inputs_1_output (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP791

The leftmost two angles measured from thin line add to the rightmost versus no two angles add to a third.

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

	COMMENTS	`This answer is independent of whether angles are measured clockwise or counter-clockwise; only a consistent choice must be made.`
	CROSSREFS	`Adjacent-numbered pages: BP786 BP787 BP788 BP789 BP790 * BP792 BP793 BP794 BP795 BP796`
	KEYWORD	`math, structure, orderedtriplet, traditional`
	CONCEPT	`addition (info \| search),` `2_inputs_1_output (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP809

Figures can be transformed into one another by smooth stretching (before and after there are the same crossroad-points; there is a curve connecting points before if and only if there is a curve connecting those points after) vs. not so.

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

	COMMENTS	`Left examples are topologically homeomorphic figures.` `For some examples one can imagine pulling the shape "out of" the 2d square in 3d in order to transform it, and then laying it flat back in the 2d square. See BP810 for the version where this is not allowed.`
	CROSSREFS	`Adjacent-numbered pages: BP804 BP805 BP806 BP807 BP808 * BP810 BP811 BP812 BP813 BP814`
	KEYWORD	`nice, math, unorderedpair, traditional`
	CONCEPT	`topological_transformation (info \| search)`
	WORLD	`two_figures_made_of_curves [smaller \| same \| bigger] zoom in left (two_homeomorphic_figures_made_of_curves)`
	AUTHOR	`Aaron David Fairbanks`

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