The On-Line Encyclopedia of Bongard Problems

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BP122

Line divides interior into two regions vs. not so.

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

	CROSSREFS	`Adjacent-numbered pages: BP117 BP118 BP119 BP120 BP121 * BP123 BP124 BP125 BP126 BP127`
	KEYWORD	`traditional`
	CONCEPT	`separated_regions (info \| search),` `interior_exterior (info \| search),` `number (info \| search),` `tiling (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

BP322

One outer outline vs. more than one outer outline.

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

	CROSSREFS	`Adjacent-numbered pages: BP317 BP318 BP319 BP320 BP321 * BP323 BP324 BP325 BP326 BP327`
	KEYWORD	`nice, precise, allsorted, traditional`
	CONCEPT	`separated_regions (info \| search),` `interior_exterior (info \| search),` `outer_outline (info \| search),` `recursion (info \| search),` `one (info \| search)`
	WORLD	`nest_shapes [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP889

Odd number of enclosed regions vs. even number of enclosed regions.

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

	COMMENTS	`The use of numbers and pictures are only a distraction.` `See BP966 for the version in which the background counts.`
	CROSSREFS	`Adjacent-numbered pages: BP884 BP885 BP886 BP887 BP888 * BP890 BP891 BP892 BP893 BP894`
	KEYWORD	`number`
	CONCEPT	`separated_regions (info \| search),` `even_odd (info \| search)`
	AUTHOR	`Thomas Joyce`

BP899

Regions in drawing (ignore background) can be coloured using three or fewer colours such that no adjacent regions are coloured the same colour vs. four colours are required.

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

	COMMENTS	`This Problem is related to the four colour theorem.`
	CROSSREFS	`Adjacent-numbered pages: BP894 BP895 BP896 BP897 BP898 * BP900 BP901 BP902 BP903 BP904`
	KEYWORD	`hard, nice, math`
	CONCEPT	`separated_regions (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Jago Collins`

BP966

Even number of white regions vs. odd number of white regions.

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

	COMMENTS	`See BP889 for the version in which the background doesn't count.`
	CROSSREFS	`Adjacent-numbered pages: BP961 BP962 BP963 BP964 BP965 * BP967 BP968 BP969 BP970 BP971`
	KEYWORD	`nice, boundingbox, number, right-null, perfect, pixelperfect, traditional, bordercontent`
	CONCEPT	`separated_regions (info \| search),` `even_odd (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP977

Two of the same object are enclosed in the same space (there is a path between them) vs. not so.

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

	COMMENTS	`An "object" is everything within some black boundary.`
	CROSSREFS	`See BP1071 for a version with only squares and with infinite nesting allowed.` `Adjacent-numbered pages: BP972 BP973 BP974 BP975 BP976 * BP978 BP979 BP980 BP981 BP982`
	KEYWORD	`nice, precise, allsorted, creativeexamples, traditional`
	CONCEPT	`separated_regions (info \| search),` `identical (info \| search),` `recursion (info \| search),` `imagined_line_or_curve (info \| search),` `same_shape (info \| search),` `same (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP1019

White space in two circles maximum vs. white space in three circles maximum.

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

	CROSSREFS	`Adjacent-numbered pages: BP1014 BP1015 BP1016 BP1017 BP1018 * BP1020 BP1021 BP1022 BP1023 BP1024`
	KEYWORD	`nice, precise, traditional`
	CONCEPT	`recursion_number (info \| search),` `separated_regions (info \| search),` `circle (info \| search),` `recursion (info \| search),` `two (info \| search),` `three (info \| search)`
	WORLD	`circles_cross [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1022

Nesting vs. no nesting.

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

	CROSSREFS	`See BP1061 for a version of this with only squares and which allows infinite nesting.` `See BP71 for a Problem about counting levels of nesting.` `Adjacent-numbered pages: BP1017 BP1018 BP1019 BP1020 BP1021 * BP1023 BP1024 BP1025 BP1026 BP1027`
	KEYWORD	`easy, nice, precise, allsorted, traditional`
	CONCEPT	`recursion_number (info \| search),` `separated_regions (info \| search),` `inside (info \| search),` `recursion (info \| search)`
	WORLD	`varied_thickness_curves_drawing [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

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