What is the best way to set up a table for a puzzle like this

Question

I need to rearrange this to form a logical sequence. One way is to just to trial and error, however since there are 5*4*3 ways this can rearrange, that is not efficient. Is there a way to number the elements so I can see a pattern clearly?

Answer 1

Basic approach. Conceding that I haven't looked too closely at this, I would proceed as follows:

There are five shapes: circle, cross, diamond, heart, and slashed ring (the "don't" symbol). There are four textures: graph paper, polka-dotted, slashed, solid. Individually, for each of these properties—shape and texture—find the pattern followed by the figures, and then that will help you put these five triplets in a sequence so that the $15$ consecutive figures obey both patterns simultaneously.

For instance, for shape, a heart is always followed by what? Which is always followed by what? For texture, graph paper is always followed by what? And so on.