The On-Line Encyclopedia of Bongard Problems

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BP559

Cross section of a cube vs. not cross section of a cube

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	COMMENTS	`All examples are solid black shapes.` `This problem is absurdly hard. It makes a good extreme example. - Aaron David Fairbanks, Nov 23 2020`
	CROSSREFS	`Adjacent-numbered pages: BP554 BP555 BP556 BP557 BP558 * BP560 BP561 BP562 BP563 BP564`
	KEYWORD	`hard, precise, allsorted, notso, stretch, challenge, left-narrow, perfect`
	CONCEPT	`cube (info \| search),` `cross_section (info \| search)`
	WORLD	`fill_shape [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP569

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`

BP576

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`

BP812

Aesthetically pleasing vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP807 BP808 BP809 BP810 BP811 * BP813 BP814 BP815 BP816 BP817`
	KEYWORD	`easy, fuzzy, abstract, notso, stretch, anticomputer, subjective, invalid, experimental, funny, dithering`
	AUTHOR	`Aaron David Fairbanks`

BP816

Cross section of a cylinder vs. not cross section of a cylinder

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

	CROSSREFS	`Adjacent-numbered pages: BP811 BP812 BP813 BP814 BP815 * BP817 BP818 BP819 BP820 BP821`
	KEYWORD	`precise, notso, stretch, unstable, perfect`
	CONCEPT	`cross_section (info \| search)`
	WORLD	`fill_shapes [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP818

Dot's position within square is center of square's position within panel vs. not so.

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	COMMENTS	`All examples in this problem are dots inside square outlines.`
	CROSSREFS	`Similar to BP1122 (the "fractal" version).` `Adjacent-numbered pages: BP813 BP814 BP815 BP816 BP817 * BP819 BP820 BP821 BP822 BP823`
	KEYWORD	`nice, notso, boundingbox, absoluteposition`
	CONCEPT	`bounding_box (info \| search),` `self-reference (info \| search),` `center (info \| search),` `distance_from_center (info \| search)`
	WORLD	`point_inside_square [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP823

Conic section (plot of solution to conic equation) vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP818 BP819 BP820 BP821 BP822 * BP824 BP825 BP826 BP827 BP828`
	KEYWORD	`notso, math, left-couldbe`
	AUTHOR	`Aaron David Fairbanks`

BP825

Ticks mark an infinite sequence of angles on circle such that each angle is the double of the subsequent angle in the sequence (angle measured from rightmost indicated point) vs. not so.

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	COMMENTS	`This is solvable; it was solved by Sridhar Ramesh.` `A full turn is considered "the same angle" as no turns; likewise for adding and subtracting full turns from any angle. All sequences of angles shown start at the rightmost tick.` `It doesn't matter whether the angle is measured clockwise or counterclockwise, as long as the choice is consistent.`
	CROSSREFS	`Adjacent-numbered pages: BP820 BP821 BP822 BP823 BP824 * BP826 BP827 BP828 BP829 BP830`
	KEYWORD	`hard, convoluted, notso, math, solved`
	CONCEPT	`sequence (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP852

Object shown below is the "limit" of the sequence above (end result after "infinite time") versus not so.

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	COMMENTS	`The conceptual limit of the sequence may not be the limit of the points in the image. For example in a sequence of halvings the limit value is never reached, so the bottom would never change color and thus its limit would not would not either.` `Sequences progress from left to right (and there is not usually a way to intuitively extend the sequence in the other direction).`
	CROSSREFS	`Adjacent-numbered pages: BP847 BP848 BP849 BP850 BP851 * BP853 BP854 BP855 BP856 BP857`
	KEYWORD	`notso, creativeexamples, perfect, infinitedetail, assumesfamiliarity, structure, contributepairs, rules`
	AUTHOR	`Aaron David Fairbanks`

BP868

Images of impossible Bongard Problems vs. images of possible Bongard Problems.

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	COMMENTS	`This fits on its own left side.`
	CROSSREFS	`See BP821 for the version with links to pages on the OEBP (instead of images of Bongard Problems), of which this fits on the left side.` `Adjacent-numbered pages: BP863 BP864 BP865 BP866 BP867 * BP869 BP870 BP871 BP872 BP873`
	KEYWORD	`less, notso, meta (see left/right), miniproblems, example, left-finite, left-full, impossible, experimental, funny, presentationinvariant`
	CONCEPT	`impossible (info \| search)`
	WORLD	`bpimage [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

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