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BP860 Finitely many copies of the shape can be arranged such that they are locked together vs. not so.
(edit; present; nest [left/right]; search; history)
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

BP865 The class of included examples is distractingly irrelevant to the solution vs. not so.
BP965
BP1105
(edit; present; nest [left/right]; search; history)
COMMENTS

Left examples have keyword "distractingworld" on the OEBP.


This is different than the kind of distraction mentioned at noisy, which means there are details that are irrelevant to the solution changing between examples.


To label a BP "distractingworld" is to judge that the type of examples are more specific than should have been necessary to communicate the same general solution idea--this involves separating out which ideas are the nice ideas the BP really ought to have been about, and which ideas seem unimportant and irrelevant. On the other hand, to label a BP "noisy" is just to notice there are extra properties varying that are independent of the solution property.

CROSSREFS

Distractingworld BPs are often arbitrary.

Adjacent-numbered pages:
BP860 BP861 BP862 BP863 BP864  *  BP866 BP867 BP868 BP869 BP870

EXAMPLE

BP1105 was created as an extreme example of this. All images in that BP show the same distractingly detailed background, irrelevant to the solution.

KEYWORD

stub, fuzzy, abstract, subjective, meta (see left/right), links, keyword

WORLD

bp [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP928 Bongard Problems about sequences vs. other Bongard Problems.
BP926
(edit; present; nest [left/right]; search; history)
COMMENTS

Zero, one, or two objects may technically form a sequence, but if ALL examples of a BP have zero, one, or two objects, we do not consider that BP to be about sequences.

CROSSREFS

See BP929 for distinction between sequences of arbitrary length and sequences of fixed length (keywords "sequence" and "fixedsequence").

Adjacent-numbered pages:
BP923 BP924 BP925 BP926 BP927  *  BP929 BP930 BP931 BP932 BP933

KEYWORD

stub, meta (see left/right), links

WORLD

bp [smaller | same | bigger]
zoom in left (sequence_visualbp)

AUTHOR

Aaron David Fairbanks

BP954 Solution could appear in a Bongard Problem that has itself as a panel vs. not so.
(edit; present; nest [left/right]; search; history)
COMMENTS

Loosely speaking, examples on the left are "Bongard Problems that can be self-similar". However, Bongard Problems with images of themselves deeply nested in boxes or rotated/flipped are not considered "self-similar"; the Bongard Problem must use itself, as-is (allowing downward scaling and ignoring pixelation), as a panel.


All examples here are in the conventional format, i.e. white background, black vertical dividing line, and examples in boxes on either side. (A more general version of this Bongard Problem might allow many formats of Bongard Problems, sorting an image left if a self-similar version is possible having the same solution and format. This more general version would no longer be tagged presentationinvariant, since sorting would not only depend on solution, but also format.)


It would hint at the solution (keyword help) to only include images of Bongard Problems that, as it stands, are already clearly categorized on one side by themselves. (That is, images of Bongard Problems that belong on one of the two sides of BP793.) It is tricky to come up with images that are categorized by themselves as it stands but that could NOT be recursively included within themselves. EX7967, EX7999, EX7995, and EX6574 are some examples.

CROSSREFS

See BP987 which narrows down the left-hand side of this BP further based on whether or not the BP could contain itself as a panel on both sides.

Adjacent-numbered pages:
BP949 BP950 BP951 BP952 BP953  *  BP955 BP956 BP957 BP958 BP959

KEYWORD

hard, stub, abstract, challenge, meta (see left/right), miniproblems, infinitedetail, presentationinvariant, visualimagination

CONCEPT fractal (info | search),
recursion (info | search),
self-reference (info | search)

AUTHOR

Leo Crabbe

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

BP981 Each column is assigned something independently; each row is assigned something independently; there is a rule that generates contents of squares from the row information and column information vs. there is a different kind of rule.
(edit; present; nest [left/right]; search; history)
COMMENTS

To clarify the solution with an example: on the left is an image of a grid where the first row features a square with three dots and a square with nine dots, and the second row features a square with four dots and square with sixteen dots. "Three" and "four" are assigned to the rows; "x" and "x squared" are assigned to the columns.


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.


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 of this Problem.


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" might be about how the images must relate to their neighbors, for example.


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

See BP979 for use of similar structures but with one square removed from the grid. Examples on the left here with any square removed should fit on the left there.

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

KEYWORD

stub, convoluted, teach, structure, rules, grid, miniworlds

CONCEPT analogy (info | search)

WORLD

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

AUTHOR

Aaron David Fairbanks

BP988 Number of dots is a power of 2 vs. not so.
(edit; present; nest [left/right]; search; history)
COMMENTS

Numbers of dots on the left can be obtained by repeatedly doubling 1 dot.

Numbers of dots on the left are the number of corners of a cube in some dimension.

CROSSREFS

Adjacent-numbered pages:
BP983 BP984 BP985 BP986 BP987  *  BP989 BP990 BP991 BP992 BP993

KEYWORD

stub, precise, allsorted, number, left-narrow, right-null, help, preciseworld

WORLD

dots [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP989 Number of dots is n factorial for some n vs. not so.
(edit; present; nest [left/right]; search; history)
COMMENTS

Zero is intentionally left out to avoid confusion (although it would fit right).

CROSSREFS

Adjacent-numbered pages:
BP984 BP985 BP986 BP987 BP988  *  BP990 BP991 BP992 BP993 BP994

KEYWORD

stub, precise, number, math, left-narrow, right-null, help, preciseworld

WORLD

dots [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP993 Net corresponds do a unique solid vs. net can be folded into multiple different solids.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP988 BP989 BP990 BP991 BP992  *  BP994 BP995 BP996 BP997 BP998

KEYWORD

stub, precise, perfect, preciseworld

CONCEPT rigidity (info | search),
3d_net (info | search),
3d_solid (info | search),
convey_enough_information (info | search)

WORLD

polyhedron_net [smaller | same | bigger]
zoom in left (polyhedron_net_unique_solid)

AUTHOR

Leo Crabbe

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