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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

BP975 Symmetric vs. Asymmetric relations between the red and blue circles.
(edit; present; nest [left/right]; search; history)
COMMENTS

Each example in this Bongard Problem consists of mini-panels containing the same arrangement of circles (ignoring colouring). Each mini-panel has a single circle highlighted in red, and possibly some circles highlighted in blue. A strict rule for this Bongard Problem could be something like "If a circle is blue in one mini-panel and red in a second mini-panel, then the red circle from the first mini-panel is blue in the second mini-panel." The relation intepretation is that a circle is related to the red circle if and only if it is coloured blue. BP973 is a similar problem.

CROSSREFS

Adjacent-numbered pages:
BP970 BP971 BP972 BP973 BP974  *  BP976 BP977 BP978 BP979 BP980

KEYWORD

convoluted, color, infodense, rules

AUTHOR

Jago Collins

BP973 Transitive vs. non-transitive relations between the red and blue circles.
(edit; present; nest [left/right]; search; history)
COMMENTS

Each example in this Bongard Problem consists of mini-panels containing the same arrangement of circles (ignoring colouring). Each mini-panel has a single circle highlighted in red, and possibly some circles highlighted in blue. A strict rule for this Bongard Problem could be something like "If a circle is blue in one mini-panel and red in a second mini-panel, then there are no blue circles in the second mini-panel that weren't already blue in the first mini-panel." The relation interpretation is that a circle is related to the red circle if and only if it is coloured blue.

CROSSREFS

Adjacent-numbered pages:
BP968 BP969 BP970 BP971 BP972  *  BP974 BP975 BP976 BP977 BP978

KEYWORD

convoluted, color, infodense, rules

AUTHOR

Jago Collins

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

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

BP970 Triangle is largest black shape vs. circle is largest black shape.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP965 BP966 BP967 BP968 BP969  *  BP971 BP972 BP973 BP974 BP975

KEYWORD

stub

CONCEPT circle (info | search),
size (info | search),
triangle (info | search),
most (info | search),
quantity_comparison (info | search)

AUTHOR

Aaron David Fairbanks

BP969 Triangle is smallest black shape vs. square is smallest black shape.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP964 BP965 BP966 BP967 BP968  *  BP970 BP971 BP972 BP973 BP974

KEYWORD

stub

CONCEPT size (info | search),
square (info | search),
triangle (info | search),
most (info | search),
quantity_comparison (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

BP965 If you place the image on top of itself so that it lines up with itself exactly within a small region, it also lines up everywhere else vs. not so.
(edit; present; nest [left/right]; search; history)
COMMENTS

Rotations are allowed. To avoid confusion about whether reflections are allowed, no examples are included on the right that require reflections to match up with themselves locally but not globally; no examples are included on the left that can match up with themselves locally but not globally using a reflection.


Only parts of ellipses are used, and only one type of ellipse per image, to make everything easier to read and reason about.

CROSSREFS

See BP1246 for a variation on this idea where instead of lining the image up with itself along arbitrarily small regions, you line the image up with itself along individual separate objects.

Adjacent-numbered pages:
BP960 BP961 BP962 BP963 BP964  *  BP966 BP967 BP968 BP969 BP970

KEYWORD

hard, precise, distractingworld, perfect

CONCEPT local_global (info | search)

AUTHOR

Aaron David Fairbanks

BP962 White vs. black.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP957 BP958 BP959 BP960 BP961  *  BP963 BP964 BP965 BP966 BP967

KEYWORD

precise, allsorted, minimal, dual, blackwhite, gap, left-finite, right-finite, left-full, right-full, left-null, finished, preciseworld, unstableworld

WORLD

[smaller | same | bigger]
zoom in left (blank_image) | zoom in right (black_image)

AUTHOR

Leo Crabbe

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