Below, different puzzles for the cage graph of the first example are created randomly by selecting one present placement, the initial state, of the animals randomly, and selecting one set of labels for the cages, the target state, randomly as well. The animals are the inner circles in the vertices. The white circle stands for no animal, an empty cage. The designations of the cages are the colors of the rings. So you have to move the inner circles in such a way that every inner circle matches the color of the surrounding ring.
The distribution of the animals is done randomly, just to create your own private puzzle. Clicking the "New Puzzle" button creates a new one, again randomly. Try to solve three of these puzzles. How many moves do you need on average?