Solving those "4 pictures cut in half and fit the squares together" puzzles

We’ve got this puzzle made up of 9 squares. Each side of each square has half a picture of a wild animal on it (Lion, Tiger, I don’t remember). Some are front half, some back half. One is supposed to fit the front to the back half of each animal in such a way that the 9 squares make one big square.

There has to be a method better than random slopping them around to figure out which matches with which such that the puzzle can be solved. Can anyone help?

Well, you can systematically slop them around. Start with the corners. Maybe for the corner, you need one with a tiger’s butt next to a crocodile’s head, and maybe there’s only three pieces that fit that one. So try the first one. That makes two new corners to work with. Try all of the pieces that can fit in those spots, and see if they can work. If not, you know that first piece isn’t one of the ones that belongs in that corner, so try one of the other two, and so on.

Or you can sometimes get clues from slight offsets in the printing, or the pattern of pixels, or the like, but that’s probably cheating.

There is no outside frame, you just have to fit the 9 pieces together in an open space, so there’s no corner to start in. I imagine I could do it if I wanted to take the time, but I was hoping there was a trick, some kind of enter 1, 2, 3, and 4 system that would produce the answer by magic.

Or mebbie not.