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

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

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

Successful moves in Tetris.

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

precise, teach, culture, pixelperfect

Leo Crabbe

All examples in this Bongard Problem are scatter plots. Each dot represents a data point.

"Positive correlation" means that when the X value increases, the Y value tends to increase as well (in the long run), while "negative correlation" means that when the X value increases, the Y value tends to decrease.

Adjacent-numbered pages:
BP1266 BP1267 BP1268 BP1269 BP1270  *  BP1272 BP1273 BP1274 BP1275 BP1276

Example TM4854 does not fit on either side because when the X value increases, the Y value stays the same.

Example TM4855 does not fit on either side because there is no correlation.

fuzzy, minimal, unwordable, teach, spectrum, dual, handed, leftright, updown, rotate, stable, hardsort, left-narrow, right-narrow

Ben

Players can only move their piece to a node connected to their current position. A win is secured by moving to a node your opponent is occupying.

Which player that can force a win in left-sorted examples can change depending on who moves first.

See BP1284 for an animated Problem about the same game.

Adjacent-numbered pages:
BP1277 BP1278 BP1279 BP1280 BP1281  *  BP1283 BP1284 BP1285 BP1286 BP1287

allsorted, unwordable, notso, teach

Leo Crabbe

In the depicted "capture game", the objective is to capture your opponent's piece by moving to a node they are occupying. Players take turns moving their pieces. You can only move to a node that is linked to yours. Optimal play can either lead to a win-lose state or a draw state.

A frame where only one black disc is visible signifies that a player has taken the other's piece, winning the game.

Adjacent-numbered pages:
BP1279 BP1280 BP1281 BP1282 BP1283  *  BP1285 BP1286 BP1287 BP1288 BP1289

teach, animated

Leo Crabbe