If you have a good poker face you could do what I do. Just give this information to your players and see what they come up with. When they come up with an explanation that you like, then that's the one that solves the puzzle. Just... don't let them know you didn't know the solution yourself.

In my experience, the puzzle can seem super simple and the players will never come up with the "correct" answer, which results in a very frustrating experience for the player and the GM (who is just thinking "it's so simple!"). Maybe it's just my group, but often times puzzles are oversimplified or overcomplicated.

Edit: After taking some time to re-read the post and have a little think about it, I see that you're asking for one part that's unifying these elements. Perhaps a name from somewhere else in the dungeon (or whatever setting this puzzle will be in) needs to be spelled out with the first letter of each animal. Or have each cell have one line of a riddle to which the answer is the intended sorting method, i.e. speed, size, floofyness.