[dementedmongoose]

Okay, Aero, first: the zombies don't rot. They do regenerate, but it's at a much decreased rate from humans. Second: No. Unless you remove the head, the brain's pretty much the ticket. Now if your zombie develops gangrene from a wound, or necrotising fasciitis, and that eradicates their brain, you need to put a bullet in its brain, or cut its head of. Third: they don't need to eat, but it's damned hard to ignore hunger pangs when your food just falls out through a hole in your gut.

The Professor isn't perfect. He's got a human enough brain, and he will cock up eventually. You can't guarantee you'll catch him in a trap, and he'll happily chew both his legs off if it gets him into Freedom. Obviously, he's never met you, so he won't see you on the walls and think "Oh, that's John Doe, he likes using bear traps, I better be on my guard about where I walk." He might notice one bear trap and figure there's more around, and he certainly understands that propane tanks go boom if you shoot 'em, but he's not perfect. He can't tell the difference from a full propane tank and an empty one, so you could easily bottleneck his troops with that knowledge. I know I'm not explaining this very well, so I'll try to simplify it. The Professor can't always see your plans at the start, but he can adapt as you go.

The Professor is smart, but he's got a disadvantage. An invader has to worry about every move he makes, he can't lose too much or low morale will cause his men to abandon him for easier food, whereas a defender only has to worry about surviving the next wave.