This is the final problem in Bongard's original collection. It is the only member of the collection that makes reference to human culture. This can be interpreted symbolically as foreshadowing that computers will be able to perform the various tasks that humans can do.

Another idea introduced by this Bongard Problem is that a Bongard Problem can teach its solution to the solver. (See keyword teach.) A large pool of examples can be used for training, as is common in machine learning.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 247.

Adjacent-numbered pages:
BP95 BP96 BP97 BP98 BP99  *  BP101 BP102 BP103 BP104 BP105

easy, nice, teach, arbitrary, anticomputer, culture, finished, bongard

Mikhail M. Bongard

Based on Google reCaptcha human verification checks.

Adjacent-numbered pages:
BP839 BP840 BP841 BP842 BP843  *  BP845 BP846 BP847 BP848 BP849

nice, teach, anticomputer, culture, color, experimental, funny

color_street_photograph [smaller | same | bigger]

Cameron Fetter

Adjacent-numbered pages:
BP857 BP858 BP859 BP860 BP861  *  BP863 BP864 BP865 BP866 BP867

less, teach, anticomputer, culture, experimental

black_and_white_photograph [smaller | same | bigger]
zoom in left (black_and_white_face_photograph)

Leo Crabbe

"Invalid Bongard Problems" are images that look sort of like Bongard Problems but aren't actually Bongard Problems.

With many examples included, this Problem might be placed somewhere to nonverbally show someone the subtler rules about what is allowed and what isn't allowed in Bongard Problems.

See BP829 for the Bongard Problem about Bongard Problems with no clear solution.

See BP522 (flipped) for a version with links to pages on the OEBP instead of images of Bongard Problems (miniproblems).

See BP829 (flipped) for a near exact copy of this Bongard Problem idea but that does not include images with two of the same boxes on either side.

Also see BP1080, which includes various different formats of Bongard Problems, distinguishing them from arbitrary images that are not Bongard Problems.

Adjacent-numbered pages:
BP963 BP964 BP965 BP966 BP967  *  BP969 BP970 BP971 BP972 BP973

teach, meta (see left/right), miniproblems, assumesfamiliarity, structure

Jago Collins

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

Adjacent-numbered pages:
BP1044 BP1045 BP1046 BP1047 BP1048  *  BP1050 BP1051 BP1052 BP1053 BP1054

teach, creativeexamples, left-narrow, right-narrow, contributepairs, fixedgrid, miniworlds

Jago Collins

Various formats of Bongard Problems frequently seen on the OEBP are showcased on the left side here.

See BP968, which distinguishes solvable Bongard Problems from other images still formatted like Bongard Problems (as opposed to this page, which distinguishes Bongard Problems from any other images.)

Adjacent-numbered pages:
BP1075 BP1076 BP1077 BP1078 BP1079  *  BP1081 BP1082 BP1083 BP1084 BP1085

notso, teach, left-narrow, right-null

Leo Crabbe

See BP919 for the version with links to pages on the OEBP instead of images of Bongard Problems.

Adjacent-numbered pages:
BP1078 BP1079 BP1080 BP1081 BP1082  *  BP1084 BP1085 BP1086 BP1087 BP1088

teach, meta (see left/right), miniproblems, presentationinvariant

boxes_bpimage [smaller | same | bigger]

Leo Crabbe

Successful moves in Tetris.

Adjacent-numbered pages:
BP1085 BP1086 BP1087 BP1088 BP1089  *  BP1091 BP1092 BP1093 BP1094 BP1095

precise, teach, culture, pixelperfect

Leo Crabbe

This is a generalisation of Bongard Problems that allows them to have any number of sides. There is a sense in which this problem is about valid vs. invalid ways of partitioning a set of examples into equivalence classes.

https://en.wikipedia.org/wiki/Equivalence_class

Adjacent-numbered pages:
BP1148 BP1149 BP1150 BP1151 BP1152  *  BP1154 BP1155 BP1156 BP1157 BP1158

abstract, teach, infodense, structure, rules, miniworlds

zoom in left

Leo Crabbe