The On-Line Encyclopedia of Bongard Problems

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

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	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`

All gears can make complete turns vs. not so.

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	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`

Equal horizontal length vs. not

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	COMMENTS	`All examples in this Problem are pairs of straight line segments.` `This problem communicates the idea of projected distance, in this case from 2D to 1D (x-axis).`
	CROSSREFS	`Adjacent-numbered pages: BP552 BP553 BP554 BP555 BP556 * BP558 BP559 BP560 BP561 BP562`
	KEYWORD	`nice, precise, allsorted, stretch, perfect, unorderedpair, preciseworld`
	CONCEPT	`projection (info \| search)`
	WORLD	`two_segments [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

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`

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`

Representations of natural mathematical objects vs. representations of arbitrary objects.

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	COMMENTS	`This is a very fuzzy definition. Some left examples arguably should be placed on the right, since the particular way they are represented is arbitrary--the Platonic solids EX6730 and primes EX6734 especially, as these show arbitrary placement and arrangement of objects. Furthermore if arbitrary representations are allowed one cannot be sure for example the right hand drawing of random numbers EX6740 does not represent "numbers" in general. Still this Bongard Problem has been solved by people.`
	CROSSREFS	`Adjacent-numbered pages: BP808 BP809 BP810 BP811 BP812 * BP814 BP815 BP816 BP817 BP818`
	KEYWORD	`fuzzy, abstract, stretch, math, solved, collective, experimental, dithering`
	AUTHOR	`Aaron David Fairbanks`

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

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	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`

Finitely many copies of the shape can be arranged such that they are locked together vs. not so.

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	CROSSREFS	`This is a generalisation of BP861.` `Adjacent-numbered pages: BP855 BP856 BP857 BP858 BP859 * BP861 BP862 BP863 BP864 BP865`
	KEYWORD	`hard, nice, stub, precise, stretch, unstable, hardsort, challenge, creativeexamples, perfect, pixelperfect`
	CONCEPT	`tiling (info \| search)`
	WORLD	`fill_shape [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

Is exact specific image (EX6205) vs. is not.

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	COMMENTS	`A spot-the-difference exercise.` `Arguably invalid (solution not simple).`
	CROSSREFS	`Adjacent-numbered pages: BP915 BP916 BP917 BP918 BP919 * BP921 BP922 BP923 BP924 BP925`
	KEYWORD	`less, precise, convoluted, arbitrary, stretch, unstable, left-finite, left-full, perfect, pixelperfect, experimental, funny`
	CONCEPT	`imperfection_small (info \| search),` `specificity (info \| search)`
	WORLD	`bmp [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Polygons where all sides are different lengths vs. Polygons where not all sides are different lengths.

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	COMMENTS	`All examples in this Problem are outlines of convex polygons.` `This is a generalisation of scalene triangles to any polygon.`
	CROSSREFS	`The left side implies the right side of BP329 (regular vs. irregular polygons), but the converse is not true.` `The left side of BP329 implies the right side, but the converse is not true.` `Adjacent-numbered pages: BP919 BP920 BP921 BP922 BP923 * BP925 BP926 BP927 BP928 BP929`
	EXAMPLE	`Any scalene triangle will fit on the left, because no two sides are equal.` `However, any regular polygon will not fit on the left, because all of its sides are equal.` `A random convex polygon will "almost surely" fit on the left.`
	KEYWORD	`nice, stretch, right-narrow, traditional`
	CONCEPT	`all (info \| search)`
	WORLD	`polygon_outline [smaller \| same \| bigger]`
	AUTHOR	`Jago Collins`

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