Right-sorted examples are called common nets.

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

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

stub, precise, 3d, perfect, preciseworld

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

Leo Crabbe

All examples in this Problem are solid concave black shapes. In this Problem, the "cavities" of a concave shape are defined to be the convex hull of the shape minus the shape itself. For example, if you take a bite out of the edge of a piece of paper, the piece of paper in your mouth is the cavity of the bitten piece of paper. The idea may be indefinitely extended, considering whether the cavities of the cavities are concave or convex, and so on.

Adjacent-numbered pages:
BP987 BP988 BP989 BP990 BP991  *  BP993 BP994 BP995 BP996 BP997

nice, precise, perfect, traditional

concave_fill_shape [smaller | same | bigger]

Jago Collins

This is a generalization of BP820.

Adjacent-numbered pages:
BP986 BP987 BP988 BP989 BP990  *  BP992 BP993 BP994 BP995 BP996

precise, allsorted, perfect

fill_shape [smaller | same | bigger]
zoom in left

Leo Crabbe

Another way of thinking about the solution is considering whether a light source placed at the center of mass of a given example would illuminate the whole shape.

Every left for this Problem would be will be a left example for both BP367 and BP368.

Adjacent-numbered pages:
BP985 BP986 BP987 BP988 BP989  *  BP991 BP992 BP993 BP994 BP995

convoluted, perfect

fill_shape_seeing_point_center_of_mass_inside [smaller | same | bigger]

Leo Crabbe

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

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

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

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 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 Problem (shown above sorted ambiguously) are cases in which the rule is not possible to deduce without seeing more squares. 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

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