The On-Line Encyclopedia of Bongard Problems

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BP931

Some number labels its own position in the sequence from left to right vs. not so.

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

	COMMENTS	`Right examples are called "derangements".`
	CROSSREFS	`Adjacent-numbered pages: BP926 BP927 BP928 BP929 BP930 * BP932 BP933 BP934 BP935 BP936`
	KEYWORD	`handed, leftright, sequence, traditional, left-listable, right-listable`
	CONCEPT	`number (info \| search),` `dot (info \| search),` `self-reference (info \| search)`
	WORLD	`dot_clusters_sequence_horizontal [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP949

Two unique distances between points vs. three unique distances between points.

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

	CROSSREFS	`Adjacent-numbered pages: BP944 BP945 BP946 BP947 BP948 * BP950 BP951 BP952 BP953 BP954`
	KEYWORD	`nice, precise, allsorted, stretch, perfect, traditional, preciseworld`
	CONCEPT	`two (info \| search),` `three (info \| search)`
	WORLD	`3_or_4_points [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP956

Nested pairs of brackets vs. other arrangement of brackets (some open brackets are not closed or there are extra closing brackets).

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

	COMMENTS	`Examples on the left are also known as "Dyck words".`
	REFERENCE	`https://en.wikipedia.org/wiki/Dyck_language`
	CROSSREFS	`Adjacent-numbered pages: BP951 BP952 BP953 BP954 BP955 * BP957 BP958 BP959 BP960 BP961`
	KEYWORD	`easy, nice, precise, allsorted, unwordable, notso, sequence, traditional, inductivedefinition, preciseworld, left-listable, right-listable`
	CONCEPT	`recursion (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

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`

BP971

Left half has more black (less white) than right half versus vice versa.

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

	COMMENTS	`A similar, but different, solution is "center of mass is on the left half vs. center of mass is on the right half."`
	CROSSREFS	`See BP972 for the version with examples rotated a quarter-turn.` `Adjacent-numbered pages: BP966 BP967 BP968 BP969 BP970 * BP972 BP973 BP974 BP975 BP976`
	KEYWORD	`nice, precise, spectrum, dual, handed, leftright, rotate, boundingbox, blackwhite, traditional, viceversa, absoluteposition, bordercontent`
	AUTHOR	`Aaron David Fairbanks`

BP972

Top half has more black (less white) than bottom half versus vice versa.

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

	COMMENTS	`A similar, but different, solution is "center of mass is above the horizontal vs. center of mass is below the horizontal."`
	CROSSREFS	`See BP971 for the version with examples rotated a quarter-turn.` `Adjacent-numbered pages: BP967 BP968 BP969 BP970 BP971 * BP973 BP974 BP975 BP976 BP977`
	KEYWORD	`precise, spectrum, dual, handed, updown, boundingbox, blackwhite, traditional, viceversa, absoluteposition, bordercontent`
	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`

BP986

Palindromes vs. not palindromes.

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

	COMMENTS	`All examples in this Problem are sequences of graphic symbols. In this Problem, a "palindrome" is taken to be an ordered sequence which is the same read left-to-right as it is read right-to-left. A more formal solution to this Problem could be: "Sequences which are invariant under a permutation which swaps first and last entries, second and second last entries, third and third last entries, ... and so on vs. sequences which are not invariant under the aforementioned permutamation."`
	CROSSREFS	`Adjacent-numbered pages: BP981 BP982 BP983 BP984 BP985 * BP987 BP988 BP989 BP990 BP991`
	KEYWORD	`nice, precise, allsorted, notso, sequence, traditional`
	CONCEPT	`element_wise_symmetry (info \| search),` `identical (info \| search),` `sequence (info \| search),` `same_shape (info \| search),` `same (info \| search),` `symmetry (info \| search)`
	AUTHOR	`Jago Collins`

BP992

Concave shapes with concave cavities vs. convex cavities

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

	COMMENTS	`All examples in this Problem are solid concave black shapes. In this Problem, the "cavities" of a concave shape are defined to be the convex hull of the shape minus the shape itself. For example, if you take a bite out of the edge of a piece of paper, the piece of paper in your mouth is the cavity of the bitten piece of paper. The idea may be indefinitely extended, considering whether the cavities of the cavities are concave or convex, and so on.`
	CROSSREFS	`Adjacent-numbered pages: BP987 BP988 BP989 BP990 BP991 * BP993 BP994 BP995 BP996 BP997`
	KEYWORD	`nice, precise, perfect, traditional`
	CONCEPT	`recursion_number (info \| search),` `recursion (info \| search)`
	WORLD	`concave_fill_shape [smaller \| same \| bigger]`
	AUTHOR	`Jago Collins`

BP1002

Vaguely self-similar (looks like self-similar fractal after one iteration) vs. not so.

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

	CROSSREFS	`See BP1004 for a Problem about conceptual self-similarity instead of visual self-similarity.` `See BP188 for a similar Problem restricted to shape outlines made of shape outlines.` `Adjacent-numbered pages: BP997 BP998 BP999 BP1000 BP1001 * BP1003 BP1004 BP1005 BP1006 BP1007`
	KEYWORD	`easy, nice, fuzzy, abstract, anticomputer, concept, traditional`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search),` `similar_shape (info \| search),` `similar (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

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