This is a generalisation of BP861.

Adjacent-numbered pages:
BP855 BP856 BP857 BP858 BP859  *  BP861 BP862 BP863 BP864 BP865

hard, nice, stub, precise, stretch, unstable, hardsort, challenge, creativeexamples, perfect, pixelperfect

fill_shape [smaller | same | bigger]

Leo Crabbe

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

stub

Aaron David Fairbanks

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

stub

Aaron David Fairbanks

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.

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

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

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

Aaron David Fairbanks

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.

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

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

dots [smaller | same | bigger]

Aaron David Fairbanks

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

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

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

dots [smaller | same | bigger]

Aaron David Fairbanks

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

stub, precise, perfect, preciseworld

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

Leo Crabbe

More specifically these solids are polyhedra, and are often called "space-filling".

There is ambiguity here regarding some nets that can be folded to make multiple different solids. For example EX8175 could correspond to a cuboid with a pyramid-like protrusion at each end, a protrusion at one end and an indent at the other, or 2 indents. Only the second of these options can tessellate 3D space. For clarity's sake examples like this are not sorted on either side.

Adjacent-numbered pages:
BP989 BP990 BP991 BP992 BP993  *  BP995 BP996 BP997 BP998 BP999

stub, precise, 3d, perfect, preciseworld

polyhedron_net [smaller | same | bigger]

Leo Crabbe

Rhetorical question: Where would the collection of left examples of this Bongard Problem be sorted by this Bongard Problem? (The question is whether these examples considered together satisfy the pattern that all the parts do, namely that the whole satisfies the pattern that all the parts do.)

See BP793 and BP1004 for similar paradoxes.

See BP1005 for the version about only numerical properties; examples in that BP would be sorted the same way here that they are there.

See BP1003 for a similar idea. Rather than the collection of collections imitating the individual collections, BP1003 is about the total combined collection imitating the individual collections. A picture showing (for example) an odd number of even-numbered groups would be sorted differently by these two BPs.

Also see BP1004, is likewise about the whole satisfying the same rule as its parts, but there the parts don't themselves have to be collections; there the parts are just plain individual objects. The panels in BP999 (this BP) should be sorted the same way in BP1004.

See BP1002, which is about only visual self-similarity instead of more general conceptual "self-similarity".

Adjacent-numbered pages:
BP994 BP995 BP996 BP997 BP998  *  BP1000 BP1001 BP1002 BP1003 BP1004

nice, stub, abstract, creativeexamples, left-narrow, rules, miniworlds

[smaller | same | bigger]
zoom in left | zoom in right

Aaron David Fairbanks

Adjacent-numbered pages:
BP1077 BP1078 BP1079 BP1080 BP1081  *  BP1083 BP1084 BP1085 BP1086 BP1087

stub, precise, allsorted

Leo Crabbe