It is not possible to start and end a Hamiltonian path at opposite angles

However, in any grid with even numbered sides,opposite corners are the same color,so it's impossible to start and end a Hamiltonian path on opposite corners.It seems like you're out of luck,unless you look at the rules carefully and notice an important exception.It's true that once you activate the switch in a contaminated room,it's destroyed and you can never go back.