"Image of Bongard Problem with solution X vs. empty image" where X is the phrase in quotes.

See BP959, BP902.

Adjacent-numbered pages:
BP948 BP949 BP950 BP951 BP952  *  BP954 BP955 BP956 BP957 BP958

nice, precise, meta (see left/right), miniproblems, overriddensolution, right-full, right-null, perfect, infinitedetail, experimental, funny

zoom in left (bp953_image) | zoom in right (blank_image)

Leo Crabbe

Examples on the left are also known as "Dyck words".

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

Adjacent-numbered pages:
BP951 BP952 BP953 BP954 BP955  *  BP957 BP958 BP959 BP960 BP961

easy, nice, precise, allsorted, unwordable, notso, sequence, traditional, inductivedefinition, preciseworld, left-listable, right-listable

Aaron David Fairbanks

See also BP955 for the other two evident possibilities.

Adjacent-numbered pages:
BP952 BP953 BP954 BP955 BP956  *  BP958 BP959 BP960 BP961 BP962

nice, abstract, solved, meta (see left/right), miniproblems, creativeexamples, assumesfamiliarity, structure, experimental

oblong_panels_bpimage_sorts_both_sides_balanced [smaller | same | bigger]
zoom in left (oblong_panels_bpimage_sorts_both_sides_stay) | zoom in right (oblong_panels_bpimage_sorts_both_sides_swap)

Leo Crabbe

Some examples are Bongard Problems with this solution.

Adjacent-numbered pages:
BP956 BP957 BP958 BP959 BP960  *  BP962 BP963 BP964 BP965 BP966

nice, precise, dual, handed, leftright, perfect, infinitedetail, both, neither, preciseworld

Aaron David Fairbanks

See BP889 for the version in which the background doesn't count.

Adjacent-numbered pages:
BP961 BP962 BP963 BP964 BP965  *  BP967 BP968 BP969 BP970 BP971

nice, boundingbox, number, right-null, perfect, pixelperfect, traditional, bordercontent

Aaron David Fairbanks

A similar, but different, solution is "center of mass is on the left half vs. center of mass is on the right half."

See BP972 for the version with examples rotated a quarter-turn.

Adjacent-numbered pages:
BP966 BP967 BP968 BP969 BP970  *  BP972 BP973 BP974 BP975 BP976

nice, precise, spectrum, dual, handed, leftright, rotate, boundingbox, blackwhite, traditional, viceversa, absoluteposition, bordercontent

Aaron David Fairbanks

An "object" is everything within some black boundary.

See BP1071 for a version with only squares and with infinite nesting allowed.

Adjacent-numbered pages:
BP972 BP973 BP974 BP975 BP976  *  BP978 BP979 BP980 BP981 BP982

nice, precise, allsorted, creativeexamples, traditional

Aaron David Fairbanks

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" can be about how the images relate to their neighbors, it can involve the position of the images in the grid, and it can involve properties of the grid considered as a whole. One square from somewhere along the edge of the grid is removed.

Intentionally left out of this Bongard Problem (or left as sorted ambiguously) are cases in which there is no clear rule, or it is not possible to deduce what the intended rule is without seeing more squares (e.g. EX8097). Due to this choice to omit those kinds of examples from the right, another acceptable solution is "it is possible to deduce the contents of the missing square once the underlying rule is understood vs. not so."

https://en.wikipedia.org/wiki/Raven%27s_Progressive_Matrices

BP1258 is very similar: whether ALL squares can be deduced from the rest.

Adjacent-numbered pages:
BP974 BP975 BP976 BP977 BP978  *  BP980 BP981 BP982 BP983 BP984

nice, notso, structure, rules, miniworlds

grid_of_images_with_rule_one_on_edge_missing [smaller | same | bigger]

Aaron David Fairbanks

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