Cat and Mice puzzle!

Hint: The walls form a closed curve, so every time you cross a wall you go from the outside area to the inside area, or vice versa.

Since the fence is a simple closed curve, and the cats are on the outside, we can tell which mice are on the inside by counting how fences a nearby cat has to cross to reach a particular mouse.

Every time you cross a fence, you go from the inside of the curve to the outside, or the reverse. If a cat and a mouse are separated by an odd number of fence sections, the mouse is safe; if by an even number the mouse may be caught.

By inspection, only one mouse is vulnerable.