More specifically, on the left:

Each row and each column is associated with a certain object or concept. There is a rule that combines the row object with the column object to give an image; it would be possible to extend with new rows/columns or delete/reorder any existing columns.

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.

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.

Similar idea that does not quite work as a solution here: any removed square could be reconstructed based on the rule vs. not.

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.

Grid of analogies vs. different kind of rule.

Images determined based on information independently assigned to rows and columns vs. different kind of rule.

Images systematically determined based on row and column vs. different kind of rule.

More specifically, on the left:

Each row and each column is associated with a certain object or concept. There is a rule that simply combines the row object with the column object to give an image. As such it would be possible to add new rows/columns or delete/reorder any existing columns.

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.

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.

Similar idea that does not quite work as a solution here: any removed square could be reconstructed based on the rule vs. not.

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.

More specifically, on the left:

Each row and each column is associated with a certain object or concept. There is a rule that simply combines the row object with the column object to give an image.

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.

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.

Similar idea that does not quite work as a solution here: any removed square could be reconstructed based on the rule vs. not.

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.

More specifically, on the left:

Each row and each column is associated with a certain object or concept. There is a rule that simply combines the row object with the column object to give an image. As such it would be possible to add new rows/columns or delete/reorder any existing columns without disrupting the rule.

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.

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.

Similar idea that does not quite work as a solution here: any removed square could be reconstructed based on the rule vs. not.

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.

More specifically, on the left:

Each row and each column is associated with a certain object or concept. There is a rule that combines the row object with the column object to give an image. It would be conceivable to add/delete/reorder rows/columns.

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.

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.

Similar idea that does not quite work as a solution here: any removed square could be reconstructed based on the rule vs. not.

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.

More specifically, on the left:

Each row and each column is associated with a certain object or concept. There is a rule that combines the row object with the column object to give an image. It would be conceivable to add/delete/reorder columns/rows.

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.

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.

Similar idea that does not quite work as a solution here: any removed square could be reconstructed based on the rule vs. not.

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.

Rule systematically determines images based on row and column vs. different kind of rule.

Rule determines images based on row and column vs. different kind of rule.

Rule determines contents of squares based on row and column vs. different kind of rule.

Rule determines images based on row and column vs. different kind of rule.

Rule determines images based on row and column vs. there is a different kind of rule.

There is a rule that determines squares based on row and column vs. there is a different kind of rule.

There is a rule that determines squares based on the row and column vs. there is a different kind of rule.

There is a rule that determines squares based on row and column vs. there is a different kind of rule.