The On-Line Encyclopedia of Bongard Problems

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Image conceptually relates to the golden ratio/Fibonacci numbers versus not so.

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	CROSSREFS	`BP800 is the metaconcept page for this concept.` `Adjacent-numbered pages: BP792 BP793 BP794 BP795 BP796 * BP798 BP799 BP800 BP801 BP802`
	KEYWORD	`abstract, math, concept, experimental`
	CONCEPT	`golden_ratio (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

Complete finite collection versus incomplete infinite collection.

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	COMMENTS	`Related to BP379 and BP380.` `EX10061 can ambiguously be taken to be self-referential as the either set of left-hand examples (which would make the right hand solution only "incomplete sets") or the class of finite sets.`
	CROSSREFS	`Adjacent-numbered pages: BP787 BP788 BP789 BP790 BP791 * BP793 BP794 BP795 BP796 BP797`
	KEYWORD	`abstract, creativeexamples, rules, miniworlds, collection`
	CONCEPT	`completeness (info \| search),` `finite_infinite (info \| search)`
	WORLD	`collection_of_objects_same_type [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

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

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	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`

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

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	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`

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

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	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`

Four regions vs. less than four regions enclosed by straight lines

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	COMMENTS	`All examples in this Problem are a number of (possibly overlapping) straight lines.`
	CROSSREFS	`Adjacent-numbered pages: BP771 BP772 BP773 BP774 BP775 * BP777 BP778 BP779 BP780 BP781`
	WORLD	`segments_cross [smaller \| same \| bigger]`
	AUTHOR	`Finn Collins`

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

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	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`

Shape outlines that aren't triangles vs. black shapes that aren't squares.

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	COMMENTS	`An example of an overriddensolution.`
	CROSSREFS	`Adjacent-numbered pages: BP565 BP566 BP567 BP568 BP569 * BP571 BP572 BP573 BP574 BP575`
	KEYWORD	`less, example, overriddensolution, experimental, funny, neither`
	WORLD	`outline_or_fill_shape [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Triangular number of dots vs. non-triangular number of dots

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	COMMENTS	`All examples in this Problem are groups of black dots.` `The nth triangular number is the sum over the natural numbers from 1 to n, where n > 0. Note: 0 is the 0th triangular number. The first few triangular numbers are 0, 1, 3 (= 1+2) and 6 (= 1+2+3)`
	CROSSREFS	`Adjacent-numbered pages: BP564 BP565 BP566 BP567 BP568 * BP570 BP571 BP572 BP573 BP574`
	KEYWORD	`nice, precise, allsorted, notso, number, math, left-narrow, left-null, help, preciseworld`
	WORLD	`dots [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

Discrete points intersecting boundary of convex hull vs. connected segment intersecting boundary of convex hull

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	COMMENTS	`If a "string" is wound tightly around the shape, does one of its segments lie directly on the shape?` `All examples in this Problem are connected line segments or curves.` `We are taking lines here to be infinitely thin, so that if the boundary of the convex hull intersects the endpoint of a line exactly it is understood that they meet at 1 point.`
	CROSSREFS	`Adjacent-numbered pages: BP559 BP560 BP561 BP562 BP563 * BP565 BP566 BP567 BP568 BP569`
	EXAMPLE	`Imagine wrapping a string around the pointed star. This string would take the shape of the boundary of the star's convex hull (a regular pentagon), and would only touch the star at the end of each of its 5 individual tips, therefore the star belongs on the left.`
	KEYWORD	`hard, nice, allsorted, solved, perfect`
	AUTHOR	`Leo Crabbe`

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