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.

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

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

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

Aaron David Fairbanks

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."

Adjacent-numbered pages:
BP981 BP982 BP983 BP984 BP985  *  BP987 BP988 BP989 BP990 BP991

nice, precise, allsorted, notso, sequence, traditional, miniworlds

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

Jago Collins

An image of this Bongard Problem fits on the left side.

See BP867 for a similar BP that sorts links to pages on the OEBP instead of images of Bongard Problems.

Adjacent-numbered pages:
BP996 BP997 BP998 BP999 BP1000  *  BP1002 BP1003 BP1004 BP1005 BP1006

stub, notso, meta (see left/right), miniproblems, funny

Aaron David Fairbanks

Since it is most intuitive to imagine spatially squishing together all the collections in the process of combining them into one big collection, avoid rules that involve relative spatial positionings of objects.

Contrast BP999, which is very similar. There, when considering the whole picture, the collections are to be treated as individual objects; here, when considering the whole picture, the collections are to be combined into one big collection. A picture showing (for example) an odd number of even-numbered groups would be sorted differently by these two BPs.

Also contrast BP1004, which is about a collection of plain objects obeying the same rule as all the objects (instead of a collection of [collections of objects] obeying the same rule as all the [collections of objects]).

See BP1006 for the version with only number-based properties. All panels in that Bongard Problem fit the same way in this Bongard Problem as well.

Adjacent-numbered pages:
BP998 BP999 BP1000 BP1001 BP1002  *  BP1004 BP1005 BP1006 BP1007 BP1008

nice, abstract, notso, creativeexamples, rules, miniworlds

[smaller | same | bigger]

Leo Crabbe, Aaron David Fairbanks

This is a version of BP999 with only numbers.

Contrast BP1006, which is very similar.

Adjacent-numbered pages:
BP1000 BP1001 BP1002 BP1003 BP1004  *  BP1006 BP1007 BP1008 BP1009 BP1010

nice, notso, hardsort, left-narrow, rules

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

Aaron David Fairbanks

Adjacent-numbered pages:
BP1020 BP1021 BP1022 BP1023 BP1024  *  BP1026 BP1027 BP1028 BP1029 BP1030

precise, allsorted, notso, handed, leftright, math, meta (see left/right), miniproblems, assumesfamiliarity, structure, preciseworld, presentationinvariant

boxes_dots_bpimage_clear_set_of_numbers [smaller | same | bigger]

Aaron David Fairbanks

Adjacent-numbered pages:
BP1022 BP1023 BP1024 BP1025 BP1026  *  BP1028 BP1029 BP1030 BP1031 BP1032

precise, allsorted, notso, arbitrary, handed, leftright, meta (see left/right), miniproblems, assumesfamiliarity, structure, preciseworld, presentationinvariant

boxes_dots_bpimage_clear_set_of_numbers [smaller | same | bigger]

Aaron David Fairbanks

Adjacent-numbered pages:
BP1023 BP1024 BP1025 BP1026 BP1027  *  BP1029 BP1030 BP1031 BP1032 BP1033

precise, allsorted, notso, handed, leftright, math, meta (see left/right), miniproblems, assumesfamiliarity, structure, preciseworld, presentationinvariant

boxes_dots_bpimage_clear_set_of_numbers [smaller | same | bigger]

Aaron David Fairbanks

Adjacent-numbered pages:
BP1024 BP1025 BP1026 BP1027 BP1028  *  BP1030 BP1031 BP1032 BP1033 BP1034

precise, allsorted, notso, handed, leftright, math, meta (see left/right), miniproblems, assumesfamiliarity, structure, preciseworld, presentationinvariant

boxes_dots_bpimage_clear_set_of_numbers [smaller | same | bigger]

Aaron David Fairbanks

Adjacent-numbered pages:
BP1025 BP1026 BP1027 BP1028 BP1029  *  BP1031 BP1032 BP1033 BP1034 BP1035

precise, allsorted, notso, handed, leftright, meta (see left/right), miniproblems, assumesfamiliarity, structure, preciseworld, presentationinvariant

boxes_dots_bpimage_clear_set_of_numbers [smaller | same | bigger]

Aaron David Fairbanks