login
Hints
(Greetings from The On-Line Encyclopedia of Bongard Problems!)
Search: all
Displaying 511-520 of 699 results found. ( prev | next )     page 1 ... 48 49 50 51 52 53 54 55 56 ... 70
     Sort: id      Format: long      Filter: (all | no meta | meta)      Mode: (words | no words)
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

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

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

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

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

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

BP979 It is possible to deduce the contents of the missing square vs. not so.
?
(edit; present; nest [left/right]; search; history)
COMMENTS

All examples show grids of squares with an image in each square, such that there is some "rule" the images within the grid obey. The "rule" can be about how the images relate to their neighbors, it can involve the position of the images in the grid, and it can involve properties of the grid considered as a whole. One square from somewhere along the edge of the grid is removed.


Intentionally left out of this Problem (shown above sorted ambiguously) are cases in which the rule is not possible to deduce without seeing more squares. Due to this choice to omit those kinds of examples from the right, another acceptable solution is "it is possible to deduce the contents of the missing square once the underlying rule is understood vs. not so."

REFERENCE

https://en.wikipedia.org/wiki/Raven%27s_Progressive_Matrices

CROSSREFS

BP1258 is very similar: whether ALL squares can be deduced from the rest.

Adjacent-numbered pages:
BP974 BP975 BP976 BP977 BP978  *  BP980 BP981 BP982 BP983 BP984

KEYWORD

nice, notso, structure, rules, miniworlds

CONCEPT convey_enough_information (info | search),
choice (info | search)

WORLD

grid_of_images_with_rule_one_on_edge_missing [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP981 Grid of analogies vs. different kind of rule.
(edit; present; nest [left/right]; search; history)
COMMENTS

On the left, each row and column could be labeled by a certain object or concept; on the right this is not so.


More specifically: on the left, each row and each column is associated with a certain object or concept; there is a rule for combining rows and columns to give images; it would be possible without changing the rule to extend with new rows/columns or delete/reorder any existing columns. On the right, this is not so; the rule might be about how the images must relate to their neighbors, for example.


All examples show grids of squares with an image in each square, such that there is some "rule" the images within the grid obey.


Left examples are a generalized version of the analogy grids seen in BP361. Any analogy a : b :: c : d shown in a 2x2 grid will fit on the left here.


To word the solution with mathematical jargon, "defines a (simply described) map from the Cartesian product of two sets vs. not so." Another equivalent solution is "columns (alternatively, rows) illustrate a consistent set of one-input operations." It is always possible to imagine the columns as inputs and the rows as operations and vice versa.


There is a trivial way in which any example can be interpreted so that it fits on the left side: imagine each row is assigned the list of all the squares in that row and each column is assigned its number, counting from the left. But each grid has a clear rule that is simpler than this.

CROSSREFS

BP1258 is a similar idea: "any square removed could be reconstructed vs. not." Examples included left here usually fit left there, but some do not e.g. EX9998.


See BP979 for use of similar structures but with one square removed from the grid.

Adjacent-numbered pages:
BP976 BP977 BP978 BP979 BP980  *  BP982 BP983 BP984 BP985 BP986

KEYWORD

nice, convoluted, unwordable, notso, teach, structure, rules, grid, miniworlds

CONCEPT analogy (info | search)

WORLD

grid_of_images_with_rule [smaller | same | bigger]
zoom in left (grid_of_analogies)

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)

WORLD

zoom in left | zoom in right

AUTHOR

Jago Collins

( prev | next )     page 1 ... 48 49 50 51 52 53 54 55 56 ... 70

Welcome | Solve | Browse | Lookup | Recent | Links | Register | Contact
Contribute | Keywords | Concepts | Worlds | Ambiguities | Transformations | Invalid Problems | Style Guide | Goals | Glossary