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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. | 
